INITIAL INVESTIGATION OF SHIP RESISTANCE

AT RIVER MOUTH AREA

MUHAMMAD NASUHA MANSOR

UNIVERSITI TEKNOLOGI MALAYSIA

INITIAL INVESTIGATION OF SHIP RESISTANCE AT RIVER MOUTH AREA

MUHAMMAD NASUHA MANSOR

A dissertation submitted in partial fulfilment of the

requirements for the award of the degree of

Master of Engineering (Mechanical − Marine Technology)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

MAY 2009

iii

To my beloved wife Nordiana binti Jamil whose sacrifice a lot during this period of

study and support that made me stronger every single day. For my family and friends

who gave their utmost support.

iv

ACKNOWLEDGEMENT

Bismillahirrahmanirrahim...

All praise to Allah SWT, the Most Gracious and Most Merciful, Who has

created the mankind with knowledge, wisdom and power. Being the best creation of

Allah, one still has to depend on other for many aspects, directly and indirectly. This

is, however, not an exception that during the course of study, I had received so much

help, cooperation and encouragement that I need to duly acknowledge.

In the first place, I would like to express my sincere appreciation to my

supervisor, Dr. Faizul Amri Adnan, for encouragement, guidance, and valuable

comments in completion of this work. Without his continuous and supportive effort,

this thesis would not have been materialised. I also came across several people who

are very nice enough to offer help in term of ideas and physical assistance.

I also would like to relay a deep and warmest gratitude to my family and in

law family for their understanding, patient and support in this period of study.

Special dedication to my beloved wife Nordiana bt Jamil who experienced the most

suffering and endure pain of sacrifice. Thank for the patient and supports.

Finally, special gratitude to my all colleagues in UniKL MIMET especially

those who directly influence my thought in this thesis. Last but not least, many

thanks for my friends who are unnamed here and were involved directly or indirectly

during my study.

v

ABSTRACT

Lateral drift is one of the phenomenons when ship operates in open sea. It is

possibly occurs due to waves and/ or wind and/ or current. In this study, the

phenomenon of lateral drift effect onto ship resistance is investigated. As the early

stage of this research, the study is focused on ship resistance prediction in calm

water condition. In executing this research, the principle that will be used is by using

the selected ship resistance prediction method as a basis. Any parameters in the

formula which are influenced by drift effect will be reviewed. In this study, two

cases are considered, namely Case 1 and Case 2. For Case 1 it is mainly considered

the factor of ship velocity influencing the total resistance with lateral drift effect. For

Case 2, other parameters are taken into account, which is length and breadth, as well

as ship velocity. Due to the presence of drift angle, the velocity is separated into

longitudinal and lateral component, and consequently, the process of total ship

resistance determination is solved separately in longitudinal and lateral as well. At

the end, the resultant of total ship resistance is determined using trigonometric

solution. Thus, this becomes the total ship resistance, RTOTAL with lateral drift effect

and it varies with the variation of drift angles. This principle of investigation

considerably as an initial step in gaining some insights about this complicated

problem. The result indicates that there is significant difference of total ship

resistance, RTOTAL produced with lateral drift effect, comparing to the condition

without lateral drift effect.

vi

ABSTRAK

Lateral drift merupakan salah satu fenomena yang berlaku ketika kapal beroperasi di

laut terbuka. Ia berkemungkinan berlaku disebabkan oleh ombak dan/ atau angin

dan/ atau arus. Di dalam kajian ini, fenomena kesan lateral drift terhadap rintangan

kapal akan disiasat. Di peringkat awal, kajian ditumpukan ke atas anggaran

rintangan kapal di air tenang. Dalam penyelesaian masalah ini, sebagai asas, prinsip

yang akan digunakan ialah dengan menggunakan kaedah anggaran rintangan kapal

sedia ada yang terpilih. Formula anggaran Holtrop dan Mennen dipilih dalam

mengambil kira kesan lateral drift terhadap rintangan kapal. Semua parameter

dalam formula ini yang dipengaruhi oleh lateral drift akan dikaji, dan dalam kajian

ini, dua kes akan diambil kira. Untuk kes 1, faktor halaju kapal yang mempengaruhi

nilai rintangan dengan kesan lateral drift hanya akan diambil kira. Untuk kes 2,

parameter- parameter yang lain selain dari halaju diambil juga kira iaitu panjang dan

lebar kapal. Disebabkan adanya sudut drift, halaju kapal di pecahkan kepada

komponen memanjang dan sisian. Oleh yang demikian, proses penentuan nilai

rintangan kapal juga akan diselesaikan secara berasingan, dalam keadaan

memanjang dan melintang. Kemudian, paduan nilai rintangan kapal akan ditentukan

dengan menggunakan penyelesaian trigonometri. Nilai paduan ini dikenali sebagai

jumlah rintangan kapal, RTOTAL dalam keadaan kesan lateral drift. Nilai ini berbeza

dengan kepelbagaian nilai sudut drift. Prinsip asas pengkajian ini adalah merupakan

langkah awal dalam memperolehi gambaran awal mengenai masalah yang rumit ini.

Keputusan yang diperolehi menunjukkan ianya terdapat perbezaan yang ketara

terhadap jumlah rintangan kapal keseluruhannya, dengan mengambil kesan kira

lateral drift, jika dibandingkan dengan keadaan tanpa kesan ini.

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATIONS iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vii

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xii

LIST OF SYMBOLS xiv

LIST OF APPENDICES xvi

1 INTRODUCTION 1

1.1 Preface 1

1.2 Problems Statement 4

1.3 Research Objectives 5

1.4 Research Scopes 5

1.7 Significant of Research 6

2 LITERATURE REVIEW 7

2.1 Introduction 7

2.2

2.3

Resistance Theory

Components of Total Hull Resistance

8

9

2.3.1 Frictional Resistance 10

viii

2.3.2 Wave Making Resistance 13

2.3.3

2.3.4

Eddy Resistance

Air Resistance

15

16

2.4 Other Types of Resistance Not Included in Total

Hull Resistance

17

2.4.1 Appendages Resistance 17

2.4.2 Steering Resistance 18

2.4.3

2.4.4

2.4.5

Wind and Current Resistance

Added Resistance Due to Waves

Increased Resistance in Shallow Water

18

19

19

2.5 Prediction of Ship Resistance 20

2.5.1 Holtrop’s and Mennen’s Method 22

2.5.2 Van Oortmerssen’s Method 26

2.5.3

2.5.4

Guldhammer’s and Harvald’s Method

DJ Doust’s Method

29

31

2.6 Lateral Drift Effect 33

3 RESEARCH METHODOLOGY 37

3.1 Introduction 37

3.2 Research Methodology 37

4 LATERAL DRIFT EFFECT 42

4.1 Introduction 43

4.2 Lateral Drift Factors 44

4.2.1

4.2.2

Current

Wind

44

45

4.3

4.4

4.5

Definition of Lateral Drift Effect

Lateral Drift Effect in Specific Case

Direction of Drift Factors

46

48

50

5 MATHEMATICAL DERIVATIONS 53

5.1 Introduction 53

5.2 Holtrop’s and Mennen’s Derivation 54

ix

6 COMPUTER PROGRAMMING 60

6.1 Introduction 60

6.2 Computer Programming Verification 60

6.3 Program Flowchart 61

6.4 Input and Output Data 61

6.4.1

6.4.2

6.4.3

User Input Data

Data in the Programming

Output Data

61

62

63

7 RESULTS AND DISCUSSION 65

7.1 Introduction 65

7.2 CASE 1: Severe Drift Effect on the Ship Total

Resistance, RTOTAL

66

7.2.1

7.2.2

7.2.3

Ship Total Resistance, RTOTAL with the

Drift Effect (due to wind)

Ship Total Resistance, RTOTAL with Current

Effect

Ship Total Resistance, RTOTAL with Lateral

Drift Effect Due to Combination of Wind

and Current (Severe Case)

70

72

73

7.3 Analysis the Effect at Other Ship Velocities 75

7.4 CASE 2: Severe Drift Effect on the Total Ship

Resistance, RTOTAL

80

8 CONCLUDING REMARKS 87

8.1 Conclusion 87

8.2 Recommendation for Future Research 88

REFERENCES

Appendices A- B

89

91- 96

x

x

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Limitation for Holtrop’s and Mennen’s method. 22

2.2 Limitation for Van Ootmersen method 28

2.3 Values of regression coefficient 29

2.4 Limitation of Guldhammer’s and Harvald’s method 30

2.5 Value for increament resistance coefficient at every

ship displacement

31

2.6 Limitation for DJ Doust method. 32

2.7 Values of parameter ‘a’ 33

3.1 Beaufort scale 46

5.1 Frictional Resistance Component due to Drift Angle, β 55

5.2 Frictional Resistance Component due to Current

Direction angle,α (In severe case)

56

5.3 Wave Making Resistance Component due to Drift

Angle, β

57

5.4 Bulbous Bow Resistance Component due to Drift

Angle, β

57

5.5 Immersed Transom Resistance Component due to Drift

Angle, β

58

5.6 Model Correlation Resistance Component due to Drift

Angle, β

58

6.1 List of data’s set in the programming 62

7.1 CASE 1: Result of Ship Total Resistance with Lateral

Drift Effect at Various Drift and Current Direction

Angles

67

xi

7.2 Resultant ship total resistance at speed 25 knots with

various drift angles

72

7.3 Comparison of differences between total ship

resistance produced in normal condition with

maximum and minimum

75

7.4(a) Total Ship Resistance Produced Due to Lateral Drift

Effect (in Severe Case) at Various Ship Velocity in

Heading Current, α = 0o

76

7.4(b) Total Ship Resistance Produced Due to Lateral Drift

Effect (in Severe Case) at Various Ship Velocity in

Starboard Beam Current, α = 90o

77

7.4(c) Total Ship Resistance Produced Due to Lateral Drift

Effect (in Severe Case) at Various Ship Velocity in

Following Current, α = 180o

78

7.4(d) Total Ship Resistance Produced Due to Lateral Drift

Effect (in Severe Case) at Various Ship Velocity in

Port Beam Current, α = 270o

79

7.5 CASE 2: Longitudinal, Lateral and Resultant Total

Resistance at Various Current Direction Angle and

Drift Angle.

82

xii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Methods of ship resistance evaluation 2

2.1 Typical curve of total hull resistance 9

2.2 Components of total hull resistance 10

2.3 Boundary layer around ship hull at LWL 13

2.4 Lord Kelvin wave pattern 14

2.5 Schematic diagram of typical ship’s wave system 15

2.6 Pressure distributions around a ship hull given by Van

Ootmersen

27

2.7 Wave system at fore and aft shoulder given by Van

Ootmersen

27

2.8 Total resistance, CT, and drift moment, -CM of single-

propeller cargo/container model for a range of drift

angle, β and Froude number, Fn

34

3.1 Flowchart of the research methodology 39

3.2 Definition of length, L and breadth, B in lateral

direction for a laterally drifting ship

41

4.1 Typical nature of lateral drift effect due to wind and/

or current on travelling ship

47

4.2 Schematic diagram of drift effect in severe case (due

to current and wind) specifically at river mouth area

49

4.3 Direction of current (for severe case) in several main

cases

51

7.1 CASE 1: Result of total ship resistance with lateral

drift effect at various drift and current direction angles

69

xiii

7.2 Total ship resistance, Rtotal at various ship speed, VS

with lateral drift angles (due to wind).

71

7.3 Schematic diagram of lateral drift effect due to current 74

7.4(a) Total ship resistance curve produced with drift effect

(in severe case) at various ship velocity in heading

current case, α = 0o

76

7.4(b) Total ship resistance curve produced with drift effect

(in severe case) at various ship velocity in starboard

beam current case, α = 90o

77

7.4(c) Total ship resistance curve produced with drift effect

(in severe case) at various ship velocity in following

current case, α = 180o

78

7.4(d) Total ship resistance curve produced with drift effect

(in severe case) at various ship velocity in port beam

current case, α = 270o

79

7.5 CASE 1: Lateral Total Resistance, RT(T) at Various

Current Direction Angle, α and Various Drift Angle,

β (at speed 25 knots)

83

7.6 CASE 1: Lateral Total Resistance, RT(T) at Various

Current Direction Angle, α and Various Drift Angle,

β (at speed 25 knots)

84

xiv

LIST OF SYMBOLS

VS Ship velocity/ speed

β Drift angle

VS (L) Longitudinal ship velocity/ speed

VS (T) Lateral ship velocity/ speed

VC Current speed

α Current direction angle

VC (L) Longitudinal current velocity/ speed

VC (T) Lateral current velocity/ speed

L Length of ship

LWL Length of waterline

LPP Length perpendicular

LR Length of run

LCB Longitudinal centre of buoyancy

B Breadth

T Draught

S Wetted surface area of the ship

Δ Ship displacement (weight)

∇ Volume displacement

CP Prismatic coefficient

CM Midship coefficient

CWP Waterplane area coefficient

CB Block coefficient

SAPP Wetted surface area of appendages

ABT Transverse sectional area of the bulb at the position where the still-

water surface intersects the stem

xv

hB Position of the centre of the transverse area ABT above the keel line

iE Half angle of entrance

AT Immersed part of transverse area of transom at zero speed

ρSW Density of salt water

νSW Viscosity of salt water

G Gravity acceleration

Rn Reynold’s number

Fn Froude’s number

FnT Froude’s number based on the transom

Fni Froude’s number based on the immersion

PE Effective power

RT Total Resistance

RTOTAL Total ship resistance with lateral drift effect

RF Frictional resistance

RAPP Appendages resistance

RW Wave- making resistance

RB Additional resistance due to presence of bulbous bow

RTR Additional pressure resistance due to immersed transom

RA Model- ship correlation resistance

RR Residuary resistance

CT Total resistance coefficient

CF Frictional resistance coefficient

CAS Steering resistance coefficient

CAA Air resistance coefficient

Ca Correlation factor

CR Residuary resistance coefficient

Corr CR Correction factor

di regression coefficient

xvi

LIST OF APPENDICES

APPENDIX

TITLE PAGE

A1 Flowchart of computer programming using

FORTAN to calculate longitudinal total

resistance with drift effect

91

A2 Flowchart of computer programming using

FOTRAN to calculate lateral total resistance

with drift effect

93

B1 Total ship resistance, RT determination in

longitudinal and lateral component with drift

effect caused by drift angle, β (due to wind)

95

B2 Total ship resistance at service speed 25 knots

with lateral drift effect due to current (4

knots) at various current direction angles.

96

CHAPTER I

INTRODUCTION

 

 

 

 

1.1 Preface

 

 

In this research, the study about one of the ship performances in actual sea is

carried out. It is about the initial investigation of ship resistance specifically at river

mouth area. This river mouth area is highlighted since one of the main effect which

experienced by a moving ship is a lateral drift. As an initial study, this effect will be

focused and taken into account onto the ship resistance. This specific case of study

is initiated due some previous researches about the effect of lateral drift on the other

ship performances. One of the remarkable studies was carried out by Faizul A. A and

Yakusawa H. (Faizul and Yakusawa, 2007), which about the influence of lateral drift

on seakeeping performance. They found out and summarized that as far the ship

motion study is concerned, the effect of lateral drift is not negligible. Due to this

finding basically motivates this initial study, which considering on the ship resistance

study. Before the discussing more about this lateral drift and the effect on ship

resistance, an overview about introduction of this topic will be outlined first.

 

 

2

Ship resistance evaluation methods

Traditional and standard series

methods

Regression based

methods (statistical methods

Computational fluid dynamics (CFD)

Direct model test

In ship design stage, there are a number of important scopes or disciplines

that need to be concerned in detailed. All of the related scopes basically with one

aim; to get an optimum performance of the ship that to be designed. For this

particular project, one of the studies will be focused and discussed in deeper, which

is the ship resistance. As we know, ship resistance study is one of the essential parts

in ship design in order to determine the effective power, PE required by the ship to

overcome the total resistance, RT and certain speed, VS. From there, total installed

power then can be calculated and determined for that ship. Prediction in preliminary

design stage is one of the important practices in ship design.

Concerning of fuel price growth basically increases the requirements to the

quality of ship resistance and propulsion study on the design stage. To evaluate the

resistance of a ship, in practice, designer has several options available. Figure 1.1 in

general summarized four basic classes of approach to the ship resistance

determination; the traditional and standard series, the regression based procedures,

the computational fluid dynamics approach and the direct model test. The choice of

method basically depend not only the capability available but also on the accuracy

desired, the fund available and the degree to which the approach has been developed.

Other than that, types of the ship and the limitation also are taking into account.

Figure 1.1: Methods of Ship Resistance Evaluation (Carlton, 1994)

3

Traditional and standard series methods considerably more reflects to the application

of the theory of ship resistance, which will be discussed more on the next chapter.

The last method is considered the most accurate among others because it use model

with geometrically similar to the ship and applicable to any kind of ships. The others

are only can be used to predict ship resistance between certain limits or only for a

ship that have similar particulars to such group.

In executing this study, there are several stages that will be approached and

discussed orderly. As well known, ship resistance can be evaluated either in calm

water or in wave’s condition. Particularly in ship design practice, for the early stage,

the prediction of ship resistance is highlighted more in calm water condition. Thus,

power required to attain a certain speed in seaway have been determined from the

still water performance after making allowance of 15 to 30% for wind or/ and waves

or/and current. The prediction is applied (early stage) basically using a numerical/

statistical/ regression prediction method. There are a number of reliable methods that

had been applied in predicting ship resistance in calm water and further discussion

about that will be outlined later on Chapter II. Besides the ship resistance prediction

in calm water, another approach is determining a ship resistance in wave. To this

extent of ship resistance evaluation, in practice, experimental data of ship resistance

in waves is necessary and contributes the most reliable and good result for predicting

ship resistance in waves. The result is taken and summarized as an added resistance,

where by subtracting the result of ship resistance in calm water with the results of

ship resistance in waves.

However, from one point of view, effects of drift angle are important for all

types of structures and vehicles, including those for land, sea, air, and space. Same

goes to ship, where practically, when ship traveling at certain forward speed in actual

sea or river, she experiences the effects of wind and current drifting forces. The ship

will move with certain drift angle, considerably in this case influences on the ship

resistance. This effect basically has not been studied in detail previously (ship

resistance prediction). It is therefore important to capture the influence of lateral drift

and investigate in ship resistance performance.

4

As far as lateral drift effects is concerned, there is a necessary and additional

steps to be taken to extent those mentioned approach (ship resistance evaluation). In

completing this research, for the first stage, ship resistance prediction in calm water

will be studied first, by investigating the lateral drift effect. Thus, since this calm

water condition is focused, the effect of lateral drift caused by wind and current will

be concerned in this study. Due to that, several methods of ship resistance prediction

will be detailed in and accompanying with basis ship resistance theory, extended

study will be carried out to consider lateral drift effect for this ship resistance

prediction (calm water). At this earlier stage of research, study and investigation of

those prediction methods will be made, and a number of parameters or elements in

those formulas will be identified and used as a basis in considering the influence of

the lateral drift effects. This principal and approach basically is used in order to get

some insight views on this topic. This could be regarded as an initiation and

invantion of research activity.

1.2 Problem Statement

In practical, one of the natures when she operates in its real environment is

traveling with the effect of current. This current effect exist either in open sea,

coupled with effect of waves and strong winds, or in calm water condition. Focusing

on calm water condition, for this present study, it can be viewed one of the area that

could contribute very significant effect is at river mouth area. This area specifically

can be seen especially during low and high tides time. One of the most important

effects when she operates in these times and this area is a lateral drift effect. Due to

this severe current effect which causes lateral drift, it considerably influences on the

ship resistance. Hence, the captain has to reconsider the power required at the desired

speed of his ship to travel at this area with a lateral drift effect. This effect basically

5

has not been studied previously and it is therefore important to capture the influence

of lateral drift and investigate in ship resistance performance.

1.3 Research Objectives

The objectives of this present study are:

1. To investigate the effects of severe lateral drift on ship resistance.

2. To propose the suitable ship resistance prediction method by taking the effect

of high speed current and/ or wind (lateral drift) into account.

3. To develop a calculation program based on the purpose ship resistance

prediction method.

1.4 Research Scopes

In ensuring this study can be completed successfully, several scopes will be

covered during completing this research. The scopes that have to be covered phase

by phase are:

1. Literature review on ship resistance theory, ship resistance prediction method

and lateral drift effect.

2. For lateral drift effect, literature is reviewed due to severe current effect, with

a bigger drift angle will be specified.

3. Correlate the effect of lateral drift in ship resistance study.

4. Since prediction of ship resistance with lateral drift effect will be focused, the

most suitable and applicable prediction method will be identified as a basis.

6

5. Derive the suitable ship resistance prediction method.

6. Develop the calculation software for predicting ship resistance with lateral

drift effect in severe case.

7. Make a comparison between the computed result of ship resistance in severe

lateral drift effect and ship total resistance in normal condition.

1.5 Significant of Research

During the design stage, designers/ naval architects perform their best effort

in achieving as accurate as possible in designing the ship. This activity definitely

includes in the ship resistance determination. Concerning this practice initially made

this research significantly necessary, especially when it is considered in specific case.

It is viewed that this effect of lateral drift could contribute very significant,

specifically at river mouth area due to existing of current effect. Due to this current

effect makes the lateral drift effect more severe, and it is believed it will influence on

the ship resistance performance. This effect basically has not been studied previously

in ship resistance point of view. Hence, by taking into account this specific condition

in ship resistance determination, a better, specific and more accurate result possibly

can be obtained at early of design stage.

CHAPTER II

 

 

 

 

LITERATURE REVIEW

2.1 Introduction

Prior to the start of the present study and development, several literature

researches have been put in focus first. The main role of these literature basically to

motivate the present study in ensuring the objectives is successfully achieved.

Regarding to that purpose, the literature research will be divided into several parts of

discussion. At first, the discussion and focus will be given onto the ship resistance

part. The discussion including the basis theory related to ship resistance and the

approach methods in predicting and evaluating ship resistance. Deeper understanding

against methods of ship resistance prediction is very important in order to put

directly the relationship with effects in lateral drift condition. The drift effects, as per

discussed earlier might be due to wind or/ and waves.

Then, in second part of the literature research, lateral drift effect will be

highlighted more, particularly which contributed to the ship resistance performance.

The objective can be successfully achieved by digesting the relationship between

ship resistance and the lateral drift effect of the ship when travelling through water.

  8

Since the literature onto the ship resistance prediction methods is carried out, the

initial investigation is highlighted in studying ship resistance with lateral drift effect.

2.1 Resistance Theory

  When a body moves through a fluid it may experiences forces opposing the

motion. As a ship moves through water and air it experiences both water and air

forces. This force is the water’s resistance to the motion of the ship, which is referred

to as “total hull resistance” (RT). This resistance force consequently is used to

calculate a ship’s effective horsepower. A ship’s calm water resistance is a function

of many factors, including ship speed, hull form (draft, beam, length, wetted surface

area), and water temperature. Total hull resistance increases as speed increases as

shown below in Figure 2.1. Note that the resistance curve is not linear. The water and

air masses may themselves be moving, the water due to currents and the air as a

result of winds. These will, in general be of different magnitudes and directions. The

resistance is studied initially in still water with no wind. Separate allowances are

made for wind and the resulting distance travelled corrected for water movements.

Unless the winds are strong the water resistance will be the dominant factor in

determining the speed achieved.

  9

Figure 2.1: Typical curve of total hull resistance

2.2 Components of Total Hull Resistance

As a ship moves through calm water, there are many factors that combine to

form the total resistance force acting on the hull. The principle factors affecting ship

resistance are the friction and viscous effects of water acting on the hull, the energy

required to create and maintain the ship’s characteristic bow and stern waves, and the

resistance that air provides to ship motion. In mathematical terms, total resistance

can be written as:

RT = RV + RW + RAA (2.1)

Where:

RT = total hull resistance

RV = viscous (friction) resistance

RW = wave making resistance

RAA = resistance caused by calm air

  10

Other factors affecting total hull resistance will also be presented. Figure 2.2

shows how the magnitude of each component of resistance varies with ship speed. At

low speeds viscous resistance dominates, and at high speeds the total resistance curve

turns upward dramatically as wave making resistance begins to dominate (Arizam,

2003)

Figure 2.2: Components of Total Hull Resistance

2.2.1 Frictional Resistance

As a ship moves through the water, the friction of the water acting over the

entire wetted surface of the hull causes a net force opposing the ship’s motion. This

frictional resistance is a function of the hull’s wetted surface area, surface roughness,

and water viscosity. Viscosity is a temperature dependent property of a fluid that

describes its resistance to flow. Although water has low viscosity, water produces a

significant friction force opposing ship motion. Experimental data have shown that

water friction can account for up to 85% of a hull’s total resistance at low speed (Fn ≤

  11

0.12 or speed-to-length ratio less than 0.4 if ship speed is expressed in knots), and

40-50% of resistance for some ships at higher speeds. Naval architects refer to the

viscous effects of water flowing along a hull as the hull’s frictional resistance

(Bertram, 2000).

The flow of fluid around a body can be divided into two general types of

flow: laminar flow and turbulent flow. A typical flow pattern around a ship’s hull

showing laminar and turbulent flow is shown in Figure 2.3. Laminar flow is

characterized by fluid flowing along smooth lines in an orderly fashion with a

minimal amount of frictional resistance. For a typical ship, laminar flow exists for

only a very small distance along the hull. As water flows along the hull, the laminar

flow begins to break down and become chaotic and well mixed. This chaotic

behaviour is referred to as turbulent flow and the transition from laminar to turbulent

flow occurs at the transition point shown in Figure 2.3 (Harold, 1957).

Turbulent flow is characterized by the development of a layer of water along

the hull moving with the ship along its direction of travel. This layer of water is

referred to as the “boundary layer.” Water molecules closest to the ship are carried

along with the ship at the ship’s velocity. Moving away from the hull, the velocity of

water particles in the boundary layer becomes less, until at the outer edge of the

boundary layer velocity is nearly that of the surrounding ocean. Formation of the

boundary layer begins at the transition point and the thickness of the boundary layer

increases along the length of the hull as the flow becomes more and more turbulent.

For a ship underway, the boundary layer can be seen as the frothy white band of

water next to the hull. Observation of this band will reveal the turbulent nature of the

boundary layer, and perhaps we can see some of the water actually moving with the

ship. As ship speed increases, the thickness of the boundary layer will increase, and

the transition point between laminar and turbulent flow moves closer to the bow,

thereby causing an increase in frictional resistance as speed increases.

  12

Mathematically, laminar and turbulent flow can be described using the

dimensionless coefficient known as the Reynolds Number in honor of Sir Osborne

Reynolds’ (1883) contribution to the study of hydrodynamics (Harold, 1957). For a

ship, the Reynolds Number is calculated using the equation below:

Rn = VL / ν (2.2)

Where:

Rn = Reynolds number

L = length (ft)

V = velocity (ft/sec)

ν = kinematic viscosity of water (ft2/sec)

For external flow over flat plates (or ship hulls), typical Reynolds number

magnitudes are as follows:

Laminar flow: Rn < 5 x 105

Turbulent flow: Rn > 1 x 105

Values of Rn between these numbers represent transition from laminar to turbulent

flow.

 

  13

Figure 2.3: Boundary Layer around Ship Hull at LWL

 

 

 

 

2.2.2 Wave Making Resistance

A ship moving through still water surface will set up a very characteristic

pattern of waves. There are essentially two primary points of origin of waves, which

are at the bow and at the stern. However the bow wave train is more significant,

because the waves generated here persist along the ship's hull. Generally the bow

waves also larger and more predominant. These wave systems, bow and stern, arises

from the pressure distribution in the water where the ship is acting and the resultant

of net fore-and-aft force is the wave making resistance. Wave making resistance is

the result of the tangential fluid forces. It’s depends on the underwater shape of a

ship that moves through water. The size of wave created shows the magnitude of

power delivered by the ship to the water in order to move forward.

  14

Figure 2.4: Lord Kelvin Wave Pattern

Lord Kelvin (1887) has illustrated a ship’s wave pattern in order to explain

the features. He considered a single pressure point at the front, moving in straight

line over the water surface. The generated wave pattern consists of a system of

transverse wave following behind the pressure point and a series of divergent waves

radiating from the same pressure point. The envelope of the divergent wave crests

makes an angle of 19° 28' for a thin disturbance travelling in a straight line,

regardless of the speed. Figure 2.4 shows the wave pattern illustrated by Lord Kelvin

(Edward, 1988).

Furthermore, the actual ship’s wave system is more complicated such that in

Figure 2.5 below. A ship can be considered as a moving pressure field sited near the

bow and moving suction field near the stern. The bow produces a series of divergent

wave pattern and also the transverse wave in between on each side of the ship.

Similar wave system is formed at the shoulder, and at the stern with separate

divergent and transverse pattern.

  15

In the case of a deeply submerged body, travelling horizontally at a steady

speed far below the surface, no waves are formed, but the normal pressures will vary

along the length. The magnitudes of the resistance reduce with increasing the depth

of a submerged body. This force will be negligible when the depth is half-length of

the body.

 

Figure 2.5: Schematic Diagram of Typical Ship’s Wave System (Edward, 1988).

2.2.3 Eddy Resistance or Viscous Pressure Resistance

In a non-viscous fluid the lines of flow past a body close in behind it creating

pressures which balance out those acting on the forward part of the body. With

viscosity, this does not happen completely and the pressure forces on the after body

are less than those on the fore body. Also where there are rapid changes of section

the flow breaks away from the hull and eddies are created. The effects can be

minimized by streamlining the body shape so that changes of section are more

gradual.

  16

However, a typical ship has many features which are likely to generate

eddies. Transom sterns and stern frames are examples. Other eddy creators can be

appendages such as the bilge keels, rudders and so on. Bilge keels are aligned with

the smooth water flow lines, as determined in a circulating water channel, to

minimize the effect. At other loadings and when the ship is in waves the bilge keels

are likely to create eddies. Similarly rudders are made as streamlined as possible and

breakdown of flow around them is delayed by this means until they are put over to

fairly large angles. In multi-hull ships the shaft bracket arms are produced wider

streamlined sections and are aligned with die local flow. This is important not only

for resistance but to improve the flow of water into the propellers.

Flow break away can occur on an apparently well rounded form. This is due

to die velocity and pressure distribution in the boundary layer. The velocity increases

where the pressure decreases and vice versa. Bearing in mind that the water is

already moving slowly close into the hull, the pressure increase towards the stern can

bring the water to a standstill or even cause a reverse flow to occur. That is the water

begins to move ahead relative to the ship. Under these conditions separation occurs.

The effect is more pronounced with steep pressure gradients which are associated

with full forms.

2.2.4 Air Resistance

Air resistance is the resistance caused by the flow of air over the ship with no

wind present. This component of resistance is affected by the shape of the ship above the

waterline, the area of the ship exposed to the air, and the ship’s speed through the water.

Ships with low hulls and small sail area will naturally have less air resistance than ships

with high hulls and large amounts of sail area. Resistance due to air is typically 4-8% of

the total ship resistance, but may be as much as 10% in high sided ships such as aircraft

carriers. Attempts have been made reduce air resistance by streamlining hulls and

  17

superstructures, however; the power benefits and fuel savings associated with

constructing a streamlined ship tend to be overshadowed by construction costs.

2.3 Other Types of Resistance Not Included in Total Hull Resistance

In addition to frictional resistance, wave making resistance, eddy resistance

and air resistance, there are several other types of resistance that will influence the

total resistance experienced by the ship.

2.3.1 Appendage Resistance

Appendage resistance is the drag caused by all the underwater appendages

such as the propeller, propeller shaft, struts, rudder, bilge keels, pit sword, and sea

chests. Appendages will primarily affect the viscous component of resistance as the

added surface area of appendages increases the surface area of viscous friction.

Appendages include rudders, bilge keels, shaft brackets and bossings, and stabilizers.

Each appendage has its own characteristic length and therefore, if attached to the

model, would be running at an effective Reynolds' number different from that of the

main model.

Thus, although obeying the same scaling laws, its resistance would scale

differently to the full scale. That is why resistance models are run naked. This means

that some allowance must be made for the resistance of appendages to give the total

ship resistance. The allowances can be obtained by testing appendages separately and

scaling to the ship. Fortunately the overall additions are generally relatively small,

  18

say 10 to 15% of the hull resistance, and errors in their assessment are not likely to

be critical.

2.3.2 Steering Resistance

Steering resistance is added resistance caused by the motion of the rudder.

Every time the rudder is moved to change course, the movement of the rudder creates

additional drag. Although steering resistance is generally a small component of total

hull resistance in warships and merchant ships, unnecessary rudder movement can

have a significant impact. Remember that resistance is directly related to the

horsepower required to propel the ship. Additional horsepower is directly related to

fuel consumed (more horsepower equals more fuel burned). A warship traveling at

15 knots and attempting to maintain a point station in a formation may burn up to

10% more fuel per day than a ship traveling independently at 15 knots.

2.3.3 Wind and Current Resistance

The environment surrounding a ship can have a significant impact on ship

resistance. Wind and current are two of the biggest environmental factors affecting a

ship. Wind resistance on a ship is a function of the ship’s sail area, wind velocity and

direction relative to the ship’s direction of travel. For a ship steaming into a 20-knot

wind, ship’s resistance may be increased by up to 25-30%. Ocean currents can also

have a significant impact on a ship’s resistance and the power required to maintain a

desired speed. Steaming into a current will increase the power required to maintain

speed. For instance, the Kuroshio Current (Black Current) runs from South to North

off the coast of Japan and can reach a speed of 4-5 knots. What is the impact of this

  19

current? For a ship heading south in the current and desiring to travel at 15 knots it is

not uncommon to have the propulsion plant producing shaft horsepower for speeds

of 18-19 knots. Therefore, the prudent mariner will plan his or her voyage to avoid

steaming against ocean currents whenever possible, and to steam with currents

wherever possible.

2.3.4 Added Resistance Due to Waves

Added resistance due to waves refers to ocean waves caused by wind and

storms, and is not to be confused with wave making resistance. Ocean waves cause

the ship to expend energy by increasing the wetted surface area of the hull (added

viscous resistance), and to expend additional energy by rolling, pitching, and

heaving. This component of resistance can be very significant in high sea states.

2.3.4 Increased Resistance in Shallow Water

Increased resistance in shallow water (the Shallow Water Effect) is caused by

several factors.

i. The flow of water around the bottom of the hull is restricted in shallow

water, therefore the water flowing under the hull speeds up. The faster

moving water increases the viscous resistance on the hull.

ii. The faster moving water decreases the pressure under the hull, causing

the ship to “squat”, increasing wetted surface area and increasing

frictional resistance.

  20

iii. The waves produced in shallow water tend to be larger than do waves

produced in deep water at the same speed. Therefore, the energy required

to produce these waves increases, (i.e. wave making resistance increases

in shallow water). In fact, the characteristic hump in the total resistance

curve will occur at a lower speed in shallow water.

The net result of resistance for ship traveling in shallow water is that it takes

more horsepower (and fuel) to meet the required speed. Another more troublesome

effect of high speed operation in shallow water is the increased possibility of running

aground.

Just as shallow water will adversely affect a ship’s resistance, operating in a

narrow waterway such as a canal can produce the same effect. Therefore when

operating in a canal, the ship’s resistance will increase due to the proximity of the

canal walls and the decrease in pressure along the ships sides is likely to pull the ship

towards the edge of the canal. The prudent mariner is advised to operate at moderate

speeds when steaming in shallow and/or narrow waters (Harvald, 1983).

2.4 Prediction of Ship Resistance

In the design stage, particularly at the preliminary stage, early estimation of

total resistance of the ship contributes an important part. It is important to predict the

total resistance of a ship during design stage for used of determination the installed

power. As far as an early estimation of total resistance is concerned, regarding to the

Figure 1.0 earlier, there are two methods of resistance evaluation is approached,

which are standard series method and regression based method. Regression based

method or also known as systematic series is a prediction method that base on the

statistical analysis of resistance results from ad-hoc testing of models in the towing

tank. The standard series prediction method is based on the testing of series of model

  21

that carried out for the resistance prediction purposes. However these methods only

applicable to be used for ship having similar characteristics. It should be emphasized

that resistance prediction is not an exact science and that the algorithms implemented

in this program, while they are useful for estimating the resistance of a hull, may not

provide exact results (Carlton, 1994).

Since early 1900s, number of studies onto prediction of ship resistance were

carried out and published. Various methods and approaches had been discovered and

apart from that, this development process is still keep on improving for better

satisfactory for the application. Particularly for the preliminary stage in ship design

process, number of prediction methods for ship resistance had been developed and

significantly applied. These variations basically applicable to various different

families of hull shapes. For example, some of the algorithms are useful for estimating

the resistance of displacement hull or planing hulls, while others are useful for

estimating the resistance of sailing boat hulls.

Prediction methods such as Van Ootmersen’s method, Holtrop’s & Mennen’s

method, Cedric Ridgely Nevitt’s Method, DJ Doust’s Method and Guldhammer’s

and Harvald’s Method are among of the significantly useful methods in solving the

study of ship resistance prediction. As a summary, most of these methods basically

considered several elements in contributing to the prediction of total resistance of the

ship. From the basis theory of ship resistance, as discussed previously, elements such

as frictional resistance, wave making resistance and other components of resistance

such as viscous pressure resistance and air resistance are viewed as major elements in

formulating and development of ship resistance prediction. All of these elements

mainly contribute as a forms and factors to correlate in ship resistance prediction.

The relationship of those factors is applied differently for each type of prediction

methods and can be discussed on the next sub- topic.

  22

2.4.1 Holtrop’s and Mennen’s Method

In 1982 Holtrop has published results of resistance and propulsion tests with

191 models of various types of ship using statistical analysis. It was found that for 95

percent of the cases the accuracy of the statistically derived formulas is satisfactory

in preliminary design work. Holtrop and Mennen extended then their method to

include the Series 64 hull forms. Also better formulas were obtained for the higher

speed ranges. After deriving formula from the statistical analysis of model data the

next step was to use the regression equation to investigate the optimum of parameters

to suit any given design requirements. The regression analysis was based on the

results for 334 models (Holtrop and Mennen, 1982).

In their approach to establishing their formulas, Holtrop and Mennen

assumed that the non-dimensional coefficients representing the components of

resistance for a hull form might be represented by appropriate geometrical

parameters, thus enabling each component to be expressed as a non-dimensional

function of the sealing parameter and the hull form. The range of parameters for

which the coefficients of the basic expressions are valid as following:

Table 2.1: Limitation for Holtrop’s and Mennen’s Method (Arizam, 2003).

Ship types Max.

Froude

No.

CP L/B B/T

Min Max Min Max Min Max

Tankers, bulk

carriers

0.24 0.73 0.85 5.1 7.1 2.4 3.2

Trawlers,

coasters, tugs

0.38 0.55 0.65 3.9 6.3 2.1 3.0

Containership. 0.45 0.55 0.67 6.0 9.5 3.0 4.0

  23

Destroyers

Cargo liners 0.30 0.56 0.75 5.3 8.0 2.4 4.o

RORO ships,

car ferries

0.35 0.55 0.67 5.3 8.0 3.2 4.0

Holtrop’s and Mennen’s method is suitable for resistance prediction of small vessel.

However, there are still errors that exist in the final result. Therefore, all the factors

below should be considered to determine the degree of uncertain parameters:

i. Increasing in Froude number which will create a greater residuary resistance

(wave making resistance, eddy resistance, breaking waves and shoulder wave) is a

common phenomenon in small ships. As a result, error in total resistance

increases.

ii. Small vessels are easily influenced by environmental condition such as wind and

current during operational.

iii. For smaller ship, the form size and ship type has a great difference.

This method only limited to the Froude number below 0.5, (Fn < 0. 5) and

also valid for TF/ LWL > 0.04. For an extrapolation that only carried out in two

dimensions, there is a correlation allowance factor in model ship that will affect

some 15% difference in the total resistance and the effective power. This method

also limited to hull form resembling the average ship described by the main

dimensions and form coefficients used in the method. Below are the procedures of

calculation ship resistance using Holtrop’s and Mennen’s method (Holtrop and

Mennen, 1982).:

i. Calculate Frictional Resistance FF CSVR 25.0 ρ=

Where 2)2(log075.0−

=Rn

CF

  24

ii. })0225.01()95.0()/(93.0{1 6906.0521448.092497.012131 lcbCCLBcck PP +−−+=+ −

iii. )14/(06.01( −+−= PPPR ClcbCCLL

When T/L>0.05

( ) 2228446.012 LTc =

When 0.02<T/L<0.05

479948.0)02.0(20.18 078.212 +−= LTc

When T/L<0.02

479948.012 =c

iv. c13 = 1 + 0.003Cstern

v. Calculate Wave- making Resistance,

( ){ }221521 cosexp −+∇= n

dnW FmFmgcccR λρ

Where 37565.107961.178613.31 )90()(2223105 −

Γ −= EiBTcc

When B/L<0.11

3333.0)/(229577.0 LBc =Γ

When 0.11<B/L<0.25

LBc /=Γ

When B/L>0.25

BLc /0625.05.0 −=Γ

vi. )89.1exp( 32 cc −=

)}31.0(/{56.0 5.13 BFBTBT hTABTAc −+=

vii. )/(8.015 MT BTCAc −=

viii. 1631

1 /79323.4/75254.1/0140407.0 cLBLTLm −−∇−=

When CP<0.8

3216 984388.68673.1307981.8 PPP CCCc +−=

  25

When CP>0.8

Cc 7067.073014.116 −=

ix. )1.0exp( 22152

−−= nP FCcm

When L3/∇<521,

c15 = -1.69385

When 512<L3/∇<1727

36.2/)0.8/(69385.1 3115 −∇+−= Lc

When L3/∇>1727

c15 = 0.0

x. Calculate λ

When L/B<12

BLCP /03.0446.1 −=λ

When L/B>12

36.0446.1 −= PCλ

xi. Calculate Bulbous Bow Resistance, )1/()3exp(11.0 25.132niBTniBB FgAFPR +−= − ρ

Where )5.1/(56.0 BFBTB hTAP −=

And 212 ]15.0)2.0(/[ VAhTgVF BTBFni +−−=

xii. Calculate Immersed Transom Resistance, 625.0 cAVR TTR ρ=

When FnT<5

)2.01(2.06 nTFc −=

When FnT≥5

c6 =0

Where 21)]/(2/[ WPTnT BCBgAVF +=

xiii. Calculate Model Ship Correlation Resistance, AA SCVR 25.0 ρ=

  26

)04.0(5.7/003.000205.0)100(006.0 42416.0 ccCLLC BA −+−+= −

When TF/L≤0.04

c4=TF/L

When TF/L>0.04

c4=0.04

xiv. Calculate Total Resistance, RTotal = RF(1+k) + RAPP + RW + RB + RTR + RA

 

This method is based on a numerical regression, which is obtained with

experiments from models of small ships, drag ships and tugboats "The Netherlands

Ship Model Basin" in Wageningen. With this method is possible to predict the

required power in small ships like trawler ships, fish boats, tugboats, etc. With a

reliability level of 95%, consequently the error in the speed range is lower than 18%.

2.4.2 Van Oortmerssen’s Method

G. Van Oortmerssen derived a mathematical model to describe the resistance

and propulsion properties of ships as function of the Froude number, Reynold

number and other general parameters for small ships such as trawlers and tugs from

random tank data. In addition, several assumptions were made for predicting

resistance and powering of small craft such as follows:

i. The approximation of the surface disturbance of the ship by a pressure

distribution consisting of a positive and a negative pressure peak is very

realistic. There are regions of high pressure at the bow and the stern, whilst

there are regions of low pressure near the shoulders. This as shown in Figure

2.6.

  27

ii. Small ship can be characterized by the absence of a parallel middle body, so

the regions of low pressure and the wave systems of fore and after shoulder

coincide and consequently the pressure distribution is as illustrated in Figure

2.7

iii. The summation of viscous resistance and wave-making resistance

representing the components of the total resistance.

Figure 2.6: Pressure distributions around a ship hull given by Van

Ootmersen

Figure 2.7: Wave system at fore and aft shoulder given by Van

Ootmersen

The range of parameters for which the coefficients of the basic expressions are as

follow:

  28

Table 2.2: Limitation for Van Ootmersen method.

Parameter Limitation

LWL 8- 80 m

L/B 3 to 6.2

B/T 1.9 to 4.0

CP 0.50 to 0.73

CM 0.70 to 0.97

LCB -7% L to +2.8% L

½ ie 10o to 46o

V/L1/2 0 to 1.79

Fn 0 to 0.50

Van Ootmersen suggested that the final form of the resistance equation is represented

by the summation of viscous resistance and wave-making resistance as follows

(Arizam, 2003).

])2(log2

075.0[

)]cos()sin([

2

2

24

232

)9/1(1

2222

Δ−+

+++=Δ

−−−−−− −−−−

RnSV

FeCFeCeCeCR

nmFn

nmFnmFnmFnT

ρ

Where

i. BLdCdCdLCBdLCBddCi WLiPiPiiii /(10 5,2

4,3,2

2,1,0,3 +++++=

miiiWLiWLiWLi CdTBdTBdCdCdBLd 11,2

10,9,2

8,7,2

6, )/(/)/( ++++++

ii. )2/(1

bPCbm −−=

or for small ships this can be represented by

)1976.2(14347.0 −−= PCm

iii. CWL is a parameter for the angle of entrance of the load waterline, ie where

)/( BLiC WLeWL =

iv. Approximation for wetted surface area is represented by:

  29

3/133/2 5402.0223.3 VLVS WL+=

Table 2.3: Values of regression coefficient

i 1 2 3 4

di,0 79.32134 6714.88397 -908.44371 3012.14549

di,1 -0.09287 19.83000 2.52704 2.71437

di,2 -0.00209 2.66997 -0.35794 0.25521

di,3 -246.45896 -19662.02400 755.186600 -9198.80840

di,4 187.13664 14099.90400 -48.93952 6886.60416

di,5 -1.42893 137.33613 -9.86873 -159.92694

di,6 0.11898 -13.36938 -0.77652 16.23621

di,7 0.15727 -4.49852 3.79020 -0.82014

di,8 -0.00064 0.02100 -0.01879 0.00225

di,9 -2.52862 216.44923 -9.24399 236.37970

di,10 0.50619 -35.07602 1.28571 -44.17820

di,11 1.62851 -128.72535 250.64910 207.25580

2.4.3 Guldhammer’s and Harvald’s Method

This method is based on a group of model resistance test results that have

been collected and analyse using International Towing Tank Conference (ITTC)

1957. The specific residual resistance coefficient CR has been expressed as a function

of Froude number, M

Mn gLWL

VF = . CR then has been plotted against Froude number

in a group according to length-displacement ratio, L/∇ 1/3. Here ∇ is the volumetric

displacement which is φ= ∇/ LBTβ. Furthermore, the resistance curves diagram is

only corresponds to vessel with standard form, which is standard position of location

of buoyancy, standard B/T, normal shaped sections, moderate cruiser stern and raked

stem. The limits of the hull form parameters covered by this method are:

  30

Table 2.4: Limitation of Guldhammer’s and Harvald’s method

Parameter

Limitation

L/∇1/3 4.0 – 8.0

Froude number Fn

0.15 – 0.45

V/√L (knots/ft)

0.5 – 1.5

Prismatic coefficient, CP

0.55 – 0.85

This method is applicable to many types of vessels that fulfill the limitation given

above. However, correction needs to be taken into consideration for ships having

different standard form such mentioned in the concept and also for hull form shape

and model-ship correlation factor, CA.

Below is the procedure of calculation ship resistance using Gulghammer’s

and Harvald’s method.

i. Calculate wetted surface area, )7.1( += BCLS BPPρ

ii. Calculate Reynold’s number, Rn = VL / ν

iii. Calculate frictional resistance coefficient, 2)2(log075.0−

=n

F RC

Residuary resistance is a function of three parameters which are L/∇ 1/3, CP and

Froude’s number, Fn

iv. Calculate parameter, 3/1∇L L

v. Calculate Froude’s number, gLV

vi. Determine the residuary resistance coefficient from the graph residuary

resistance coefficient against speed- length ratio

vii. Calculate increment resistance coefficient,

23 )(log1.0log5.010 ∇−∇=RC

viii. Calculate CR correction for deviation from standard B/T= 2.5

  31

))(0875.01.1

(1090,1 23 L

LCBL

LCBCCFnCCorr Std

PPR −

−+=Δ

Where 094.044.0 −= FnL

LCBStd

xv. Calculate air and steering resistance, CAAS = CAA + CAS

ix. Calculate total resistance coefficient, CT

CT = CR + CF + CA + Corr1 + Corr2 + CAAS

and values for increment resistance can be referred to table 2.9 as a function

of ship displacement

Table 2.5: Value for increment resistance coefficient at every ship

displacement

Displacement (tonne) CA (10

-3)

1000 0.6

10000 0.4

100000 0

1000000 -0.6

2.4.4 DJ Doust’s Method

DJ Doust’s method is a method that yields a regression equation that

expresses ship resistance for a particular ship type in term of certain basic form

parameters at any required Froude number. Evaluation of this regression equation

for specific combinations of form parameters provides corresponding estimates

of resistance for the vessel under consideration. Those parameters are L/B, B/T,

Cm, Cp, LCB and ½ αo

e. All of these six design parameters can be calculated at an

early stage of the design. Doust has plotted the graph of changes in all this

  32

parameter for the standard ship length (200 ft). DJ Doust’s method is applicable

to predict the resistance for fishing vessel and other ship that fulfill the limitation

given above. However, correction needs to be taken into consideration for ships

having different length compare to the standard ship length (200 ft). Table 2.5

shows the limitation for DJ Doust resistance prediction method (Arizam, 2003).

Table 2.6: Limitation for DJ Doust method.

Parameter Limitation

L/B 4.4 – 5.8 B/T 2.0 – 2.6 Cm 0.81 – 0.91 Cp 0.6 – 0.7 LCB 0% - 6% aft of midship

½ αo

e 5o – 30o

Procedures of calculation for DJ Doust method are as follows (Arizam, 2003).

i. Calculate three parameters required to determine factors used to calculate

residuary resistance for the ship having standard length, 200 ft. These

parameters are L/B, B/T and LV /

ii. Calculate three factors used to calculate residuary resistance using graph

given. These three factors are F1 = f (CP, B/T), F2 = f(CP, LCB) and F’3 =

f(CP, ½ αoe, L/B)

iii. Calculate residuary resistance, CR(200) = 100a(CM-0.875). The parameter

‘a’ is a function LV / and given by Table 2.6.

iv. Calculate residuary resistance, CR(200) = F1 + F2 + F’3 + F6

v. Calculate 3/2!

0935.0Δ

= SS

vi. Calculate LVL /05.1'=

vii. Calculate Froude’s skin friction correction

viii. Calculate 3)200( )/200( LBPΔ=Δ

  33

ix. Calculate 3/1)200(

1)5.152(Δ

×= SFCδ

x. Calculate residuary resistance for the new ship, 1)200()( δ+= RNewR CC

xi. Calculate total resistance, L

VCR NewR

T

2)( Δ

=

Table 2.7: Values of parameter ‘a’

V/√L

a

0.8 -0.045 0.9 -0.053 1.0 -0.031 1.1 -0.035

2.5 Lateral Drift Effect

Study about this lateral drift effects basically is initiated from successful

study about the other ship performance that had been carried out before. The

previous study discussed the motion of the ship which influenced by the effect of

lateral drift, performed by Faizul A. A. (Faizul, 2006). The study of hydrodynamic

forces and ship motions were carried out for various hull drift angles in regular head

and beam waves and was found contributed significant differences and effects. The

effects which influence ship performance in lateral drift condition such as amplitude

of sway, roll and yaw motion is confirmed that is not negligible. Due to that

relationship basically motivated further study on the effect of lateral drift,

specifically for this case, onto ship resistance.

On top of that, another earlier study and investigation about the relationship

between lateral drift effect and ship resistance was produced. (Longo and Stern,

  34

2001) From the investigation onto the Series 60, with CB = 0.6 single-propeller

cargo/container model ship flow, they concluded that resistance increases linearly

with angle of drift for all Froude number, Fn. And the result of the investigation is

represented by the Figure 2.8

Figure 2.8: Total resistance coefficient, CT, and drift moment coefficient, -CM of

single- propeller cargo/container model for a range of drift angle, β

and Froude number, Fn (Longo and Stern, 1999)

 

CHAPTER III  

 

 

 

RESEARCH METHODOLOGY

 

 

 

 

3.1 Introduction

Upon completion of this research, a proper and sequence steps are developed

in determining its successfulness. Concerning the earlier objectives and scopes, the

research is divided into two parts. The first part of the research is carried out in

semester one and the second part of the research is performed in the second semester.

3.2 Research Methodology

As for the first part of the study, the research work began with the

understanding and familiarization of the background and conducting literature review

on the ship resistance fundamental and theory, methods for predicting ship resistance

as well as effect of lateral drift in ship resistance. All those materials of literature

review are obtained through several different sources such as books, journals also

electronic resources such as e-journal, internet, websites and online materials.

  38

Consequently, with familiarization of research topic, and understanding the

related and useful literature, in the second part, the next step is to identify and

investigate the suitable parameters or factors in ship resistance prediction that can be

correlated with the effect of lateral drift. This approach, will be the main principle of

this research. It was decided purposely to get the first insight in relating the ship

resistance determination with the effect of lateral drift. At this stage, it mainly will

bring to the mathematical modification/ derivation of ship resistance prediction with

lateral drift effect. A number of methods for ship resistance prediction will be

reviewed and modified to correlate with lateral drift effect. The modified

mathematical ship resistance prediction will then be developed in calculation

program for further analysis. For this initial investigation, Microsoft Excel and

FORTRAN program can be seen capable to be applied for calculation program. From

there, the computed results can be analyzed by comparing the resistance performance

between with and without lateral drift effect. Also the comparison with lateral drift

effect can be investigated between forward speed and lateral speed on ship

performance. The flow of the research methodology as described above can be

referred to the Figure 3.1.

  39

Figure 3.1: Flowchart of the research methodology

Based on the sequence of flow of the research methodology, it can be

summarized that several main activities will be carried out in ensuring objectives and

outcomes of this study are successfully achieved. The main activities are:

i. Identifying the applicable and suitable ship resistance prediction

method

ii. Familiarizing and specifying the lateral drift condition

iii. Derivation of ship resistance prediction formula with the effect of

high speed current and/ or wind

Identifying of Problem Statement

Literature Review

Ship Resistance Theory/ Ship Resistance Prediction

Lateral Drift Effect (River Mouth Area)

Identifying Applicable Ship Resistance Prediction Method

Mathematical Derivation

Calculation Program

Data Gathering/ Data Analysis

  40

iv. Computer Programming Development

All these summarized activities are explained in detail separately in the next

Chapters.

In deriving the ship resistance prediction method by taking the lateral drift

effects into account, there have two main methodologies that will be used, which are

specified as Case 1 and Case 2. The methodologies applied are as follows;

i. Case 1; Effects of Ship Speed

• In this case, the assumption made is the drift effect due to drift angle

considerably only has an effect on the ship velocity, VS.

• Due to that, the ship velocity, VS is broke down into two separate

components which are longitudinal component, namely as

longitudinal ship velocity, VS(L) and lateral component, known as

lateral ship velocity, VS(T).

 

• The detail discussion about Case 1 is explained in the next Chapters,

which in Chapter IV and Chapter V.

ii. Case 2; Effects of Ship Speed, Length and Breadth

• In this case, the assumption made is drift effect due to drift angle

considerably only has the effect on ship velocity, VS, length, L and

breadth, B of the ship.

• Similarly to the Case 1, the ship velocity, VS is broke down into

separate components which are longitudinal component, namely as

longitudinal ship velocity, VS(L) and lateral component, known as

lateral ship velocity, VS(T).

  41

• The ship length, L and breath, B values basically are inverted in lateral

component. The explanation for the Case 2 can be referred to the

Figure 3.2.

 

Figure 3.2: Definition of length, L and breadth, B in lateral direction for a

laterally drifting ship

Referring to the Figure 3.2, in longitudinal direction, the value of ship

length and breadth certainly similar to the original ship coordination. This is

because the direction of longitudinal velocity is the same as ship direction

without lateral drift effect. In lateral direction, if we consider the direction of

lateral speed, then the ship length becomes a ship breadth while the ship

breadth becomes a ship length. The different of speed direction cause the

changing values between ship length and breadth.

In Case 2, the main problem is due to the unsymmetrical of ship form,

which possibly will bring the assumption and results slightly difference.

However, for comparison purpose with the result in Case 1, the result for

Case 2 will be analyzed as well. Both detail discussion about the results and

analysis will be presented in the Chapter VI later.

Longitudinal velocity, VS (L)

L

B

B

L

Lateral velocity, VS(T)

CHAPTER IV

 

 

 

 

LATERAL DRIFT EFFECT

 

 

 

4.1 Introduction

In practical, when ship travels in real nature, there have several elements of

nature which considerably cannot be neglected and will influence its operation.

These environment elements which acting on the operated ship could contribute to

the drift effect, which certainly will influence the ship performance. Before

discussing further about the definition of the lateral drift effect, as well as its detail, it

is certainly to overview first about the possible causes of lateral drift effect. These

causes are essential to be identified in comprehending entirely the lateral drift effect.

4.2 Lateral Drift Factors

When dealing with real nature operation, there are several major factors or

sources which can possibly cause a drift effect, depending on the situation. In

general, lateral drift effect can be caused by individually or combination of action of

following factors;

 

 

44

i. Waves

ii. Current

iii. Wind

However, as far as the main scope is concerned (as outlined earlier) the

concentration is given for the case of operated ship in calm water. Due to that, in this

study the effect of lateral drift due to waves is excluded. Due to this, it considerably

can be said this lateral drift effect is caused by combination these following factors;

i. Current and/ or

ii. Wind

4.2.1 Current

Current, in general is defined in two separate types, namely ocean current,

and tidal current. Firstly, ocean current basically is continuous and generated by the

forces acting upon the water, such as the earth rotation, wind, temperature and

salinity differences. Current in the upper layers of the ocean or surface current are

mainly generated by the atmospheric wind system over the sea surface. Surface

current generally restricted to the upper 400 meters of the ocean.

The ocean current is also generated by the heat exchange at the sea surface

together with the salinity changes, which preferably referred as thermohaline current

or deep ocean current. These currents, which flow under the surface of the ocean and

are thus hidden from immediate detection also called as submarine rivers.

Secondly, the other types of current, called tidal current basically is caused by

the gravitational pull of the moon and the sun. This type of current preferably can be

 

 

45

seen at river, especially river mouth. In coastal region, this tidal current is obtained

has a high speed current. In fact, speed between 2 to 3 knots or more certainly can be

measured. Specifically referring to this research scopes, this type of current as well

as the area will be mainly focused for this study.

4.2.2 Wind

A ship sailing on a smooth sea and in still air experiences air resistance but

this is usually negligible and it may become appreciable only if wind is appear.

Although the wind speed and direction are never constant, a constant speed and

direction are usually assumed. The main influence of the wind is through the waves it

generates on the surface of the sea. The effect of waves it generates depends on it

velocity, the time it acts and the distance over which it acts

The strength of wind is classified by the Beaufort Scale. This scale numbers

of 0 to 12 were introduced was introduced in 1806. Scale 0 referring to a calm water

and scale 12 to a wind of hurricane force. There were no specific winds speeds

related with these numbers but the values have now been adopted internationally.

The values of the scale are shown in Table 3.1.

 

 

46

Table 3.1: Beaufort Scale (Edward, 1988).

4.3 Definition of Lateral Drift Effect

First of all, when discussing about the lateral drift effect onto the ship, we

need to clarify the definition as well as the coordination of the traveling ship with

lateral drift effect. The basic feature of traveling ship with lateral drift effect are

shown in Figure 4.1.

Number Description Limits of Speed

Knots m/s

0 Calm 0-1 0-0.3

1 Light air 1-3 0.3-1.5

2 Light breeze 4-6 1.6-3.3

3 Gentle breeze 7-10 3.4-5.4

4 Moderate breeze 11-16 5.5-7.9

5 Fresh breeze 17-21 8.0-10.7

6 Strong breeze 22-27 10.8-13.8

7 Near gale 28-33 13.9-17.1

8 Gale 34-40 17.2-20.7

9 Strong gale 41-47 20.8-24.4

10 Storm 48-55 24.5-28.4

11 Violent storm 56-63 28.5-32.6

12 Hurricane 64- and over 32.7 and over

 

 

47

Figure 4.1: Typical Nature of Lateral Drift Effect Due to Wind and/ or Current

on Traveling Ship

In general, the condition of ship travels from point O to A represents as an

intended course with speed, VS, which traveling completely in longitudinal direction.

At this condition, which no lateral drift effect, speed longitudinally, VS (L) is similar to

the ship’s speed, VS. This course represents the condition of traveled ship without

effect of lateral drift (ideal travel). The other condition (real sea) can be referred to

the ship which travels from point O to point B. It represents the condition where the

ship experiences the effect of lateral drift with angle β due to some reasons. It is

known as an actual course and the traveled ship is drifted with the ship speed, VS

becomes the average speed. This condition was happened due to the lateral drift

force acting on the ship which produced lateral speed, VS (T). Another component of

speed produced due to the drifting effect is longitudinal speed, VS (L). As initial

finding, these components of speed basically leads as part of the elements/ factors

that will be investigated further in the next phase in correlating the effect of lateral

drift in ship resistance prediction. This effect is found has not been studied in detail

previously, particularly in ship resistance prediction. For the early stage of study,

concentration is put in considering this effect in prediction method of ship resistance

in calm water condition.

Vs(L

Vs 

Vs(T

O 

A 

B 

Wind and/ or current 

β

 

 

48

4.4 Lateral Drift Effect in Specified Case

Concerning the investigation in calm water condition, the lateral drift effect

mainly is specified caused by the wind action. The action of wind naturally affects

the traveled ship and produced the drift angle. It produces a range of drift angles,

which represented by the β sign However, must be borne in mind that this action of

wind is not able to give the extreme effect of drift onto the ship. The effect of drift

(drift angle) is considerably small and has the limitation. Full scale measurement of a

ship drift angle using GPS shows that the magnitude is about 10 degrees even though

the wind speed is not so strong (Tanaka, 2003). In this case, the maximum drift

angle, β is taken up to 10 deg. Apart of the wind factor, as far as the main research

scopes and objectives are concerned, the lateral drift effect in this study is specified

in the case of severe lateral drift effect. In detailing more about this severe lateral

drift study, particularly onto ship resistance performance this drift effect which is

caused by wind is considered incorporating with the other element, which is due to

the high speed current.

This current is a tidal current and is said brought a severe case onto the lateral

drift effect due to the existing of the high current velocity, VC. This current velocity,

is known sometimes produces relatively higher speed at certain time and angle of

directions, and could give significant effect onto ship resistance performance. Due to

that, as mentioned earlier, the specific case of river mouth area is concerned. The

river mouth is focused, since it is one of the sources which could provide significant

current effect and consequently could cause more severe effect of lateral drift.

Moreover, severe effect of current particularly can be considered during low and

high tides, due to its flow and velocity at this period. During ebb and flood at typical

river mouth region, the velocity of the current is measured can be up to 4 knots

(2.058 m/s), depending on the situation and place. Depending on the direction and

coordination of both current action and ship’s travel, a significant lateral drift effect

might be happened and the overview of this severe lateral drift situation is simulated

and shown in Figure 4.2.

 

 

49

 

 

50

Besides she is experienced by the drift effect due to wind, in severe case, the drift

effect also is incorporated with the current acting in various direction angles. This

current direction angle is represented by α and at certain α, it might contribute the

significant drift effect in ship resistance performance.

.

4.5 Direction of Drift Factors

In reviewing the condition of lateral drift effect in severe case as visualized in

Figure 4.2, especially due to current factor, it can be observed that there are various

possibilities of acting direction. In this severe case, the drifted ship due to wind (with

a small drift angle, β) is experienced by the various direction of current as well,

possibly ranging from α= 0o up to 360o. To investigate more specific these various

direction angles, which is due to current, new terms of direction is created and it can

summarized in several main cases below

i. Heading current; when current experienced at 0o or 360o direction

ii. Beam current (starboard); when current experienced at 90o direction

iii. Following current; when current experienced at 180o direction

iv. Beam current (port); when current experienced at 270o direction

These cases also are illustrated in Figure 4.3

 

 

51

Vs

Longitudinal axis, x

Lateral axis, y

Beam current (Stbd)

Beam current (Port)

Heading current

Following current

Vc

β

Figure 4.3: Schematic Diagram of Current Direction (for severe case) in

Several Main Cases

Figure 4.3 was illustrated the condition of severe case of drift effect where

the drifted ship at drift angle, β is then together experienced with the current action.

This particular condition, which is due to the combination of two drift components

considerably called as severe case of drift effect. In addition, it is specifically

investigated in several main cases, namely as following current, beam current (either

port or starboard) and following current.

In general, heading and following current, does not have effect of drift

because the current experiences in same direction of ship axis (longitudinally). In

these cases, however the effect of lateral drift is significantly can be seen at the total

ship resistance produced. The traveled ship at these cases possibly produced extra of

 

 

52

less total resistance, and this will be discussed in detail in the next chapter. On the

other hands, in the case of beam current (port or starboard), it illustrated that the

current experiences entirely in lateral direction. The effect of severe lateral drift

possibly might occur significantly in the beam current case. This will be discussed

more detail as well later.

From one point of view, it is concerned that this effect can be taking into

account and correlated with the study of ship performance, specifically in this

particular case, ship resistance. It possibly can allocate room for element or effect of

lateral drift to be considered in ship resistance. It is therefore important to capture the

influence of lateral drift and investigate in ship resistance. More detail about this

investigation will be discussed in next chapter.

 

 

47

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.2: Schematic Diagram of Drift Effect in Severe Case (due to Current and Wind) Specifically at River Mouth Area 

x

y

x

y

Vs(L)

Vs(T)

Vs Wind effect

Current

Vc

Current direction angle, α

α 

Up to 360o current direction angle

CHAPTER V  

 

 

 

MATHEMATICAL DERIVATIONS

 

 

 

 

5.1 Introduction

As discussed in the earlier chapter of this ship resistance study, which

incorporate with the effect of lateral drift due to wind and/ or current (for severe

case) as the main mission, an initial investigation will be concentrated first. As the

early phase, the study about this ship resistance by taking the lateral drift effect is

developed by approximate resistance prediction method. At this stage, method

approached by Holtrop and Mennen is selected due to wider range of types, sizes and

limitation of ships/ vessels can be applied.

5.2 Holtop’s and Mennen’s Derivation

As far as ship resistance prediction is concerned, the original ship resistance

prediction formula which was developed by Holtrop and Mennen (1982) is used as

the main reference and guidance.

  54

RTotal = RF(1+k) + RAPP + RW + RB + RTR + RA (5.1)

Where;

RF : frictional resistance according to the ITTC 1957 friction formula

(1+k) : form factor describing the viscous resistance of the hull form in relation to RF

RAPP : resistance of appendages

RW : wave- making and wave- breaking resistance

RB : additional pressure resistance of bulbous bow near the water surface

RTR : additional pressure resistance of immersed transom stern

RA : model- ship correction resistance

Base on this mathematical formulation, together with the literatures, the

effect of lateral drift in the ship resistance prediction using the method is investigated

and developed. In deriving the ship resistance prediction with lateral drift effects

formula, it is determined that the element/ parameter of ship’ velocity, VS principally

is the main point of concerned. It is viewed that due to the severe lateral drift which

is caused by the wind and/ or current, the vector of the ship’s velocity is modified,

depending on the drift angle produced, β. As a result, there exists components of

velocity, which represented by the longitudinal velocity, VS (L) and lateral velocity, VS

(T). The drift angle, β presents due to the effect of drift, and it will be the main

variables in influencing the velocity’s components. With the presence of lateral drift

effect, it will modify the parameter of ship velocity (into longitudinal and lateral

component) in the Holtrop’s and Mennen’s, and consequently, the related equations

with the velocity parameter will be modified as well.

Modifying the existing formulae of the selected ship resistance prediction

method, the ship’s velocity, VS parameter (due to the action of drift angle, β) started

with the Frictional Resistance, RF. The Frictional Resistance, RF is broke down into

  55

longitudinal component, RF (L) and lateral component, RF (T). With the same concept

of frictional resistance determination, the ITTC 1957 is applied in determining the

Frictional Resistance longitudinally and laterally.

Table 5.1: Frictional Resistance Component due to Drift Angle, β

FF CSVR 25.0 ρ=

2)2(log075.0−

=Rn

CF

νVLRn =

Longitudinal Component Lateral Component

FSLF CSVR 2)( )cos(5.0 βρ=

2)2(log075.0−

=n

F RC

νβ LVR S

n)cos(

=

FSTF CSVR 2)( )sin(5.0 βρ=  

2)2(log075.0−

=n

F RC  

νβ LVR S

n)sin(

=  

Besides the effect of lateral drift (drift angle, β) due to wind, when

concerning the case of severe effect, there has another element that need to be

considered. The significant lateral drift effect (severe case) which is caused by

current is to be highlighted as well. This current element is said gave a severe case in

lateral drift due to its velocity which acts onto the moving ship. As a result, a part of

Frictional Resistance, RF due to ship velocity, VS, it is identified that there has

additional frictional resistance interacts with the ship’s hull which is due to the

velocity of current, VC. It is known as Frictional Resistance due to current velocity,

RF(C). The value will be taken into account and combined with the existing Frictional

Resistance due to ship’s velocity, RF(S). The additional resistance which due to the

current is said only affects at this frictional resistance component since at the other

components of resistance, namely appendages resistance (RAPP), wave- making

resistance (RW), bulbous bow resistance (RB), immersed transom resistance (RTR) and

model- ship correlation resistance (RA) the effect is not so significant. It is found that

  56

the values produced by these components of resistance are very small and

considerably neglected.

Frictional Resistance due to current, RF(C), mainly is determined depending on

the current velocity, VC, as well as the current direction angle. In this study, current

direction angle is the direction of the current (with its velocity) acting on the moving

ship and it is represented by α. The various values of current direction angle, α will

break down the current velocity components into longitudinal current velocity, VC (L)

and lateral current velocity, VC (T). Thus, it also will give the various effect of lateral

drift (severe) with different current direction angle. Similarly applying the ITTC

1957 of frictional coefficient, the additional frictional resistance RF(C), which is due

to the current velocity (longitudinally and laterally) is considered and determined as

followed.

Table 5.2: Frictional Resistance Component due to Current Direction angle,α

(In severe case)

FCF CSVR 25.0 ρ=

2)2(log075.0−

=n

F RC

νLVR C

n =

Longitudinal Component Lateral Component

FCLFC CSVR 2)( cos5.0 αρ=

2)2(log075.0−

=n

F RC

να LV

R CLCn

cos)( =

FCLFC CSVR 2)( sin5.0 αρ=  

2)2(log075.0−

=n

F RC  

να LV

R CLCn

sin)( =  

  57

By referring to the main reference of ship resistance prediction method, the

other component of resistance which will be influenced by the modified ship’s

velocity is the wave making and wave breaking resistance, RW. In RW calculation, the

component of ship’s velocity mainly influences the Froude’s number, Fn parameter

and also coefficient of m2 as shown below.

Table 5.3: Wave Making Resistance Component due to Drift Angle, β

( ){ }221521 cosexp −+∇= n

dnW FmFmgcccR λρ

Longitudinal Component Lateral Component

νβ LV

F SLn

)cos()( =

νβ LV

F STn

)sin()( =  

)1.0exp( 22152

−−= nP FCcm  

Longitudinal Component Lateral Component

νβ LV

F SLn

)cos()( =

νβ LV

F STn

)sin()( =  

The other component of resistance prediction which is modified due to the ship’s

velocity parameter is called additional pressure resistance of bulbous bow near the

water surface, or indicated as RB. In this component of resistance, it is affecting the

parameter of Fni and the modified equation related as followed;

Table 5.4: Bulbous Bow Resistance Component due to Drift Angle, β

)1/()3exp(11.0 25.132niBTniBB FgAFPR +−= − ρ

212 ]15.0)2.0(/[ VAhTgVF BTBFni +−−=

Longitudinal Component Lateral Component

212

)(

])cos(15.0)2.0

(/[)cos(

β

β

SBT

BFSLni

VA

hTgVF

+−

−=

212

)(

])sin(15.0)2.0

(/[)sin(

β

β

SBT

BFSTni

VA

hTgVF

+

−−= 

  58

Same goes to the resistance component due to the additional pressure resistance of

immersed transom stern, RTR. The additional resistance due to the immersed transom

part is modified due to the modified c6 coefficient, which is influenced by the FnT as

described below.

Table 5.5: Immersed Transom Resistance Component due to Drift Angle, β

625.0 cAVR TTR ρ=

when FnT<5

)2.01(2.06 nTFc −=

when FnT≥5

c6 =0

Longitudinal Component Lateral Component

21)]/(2/[)cos( WPTnT BCBgAVF += β 21)]/(2/[)sin( WPTnT BCBgAVF += β

The ship’s velocity also one of the parameters in predicting the model-ship

correlation resistance, known as RA. Due to that, it also modifies the model-ship

correction resistance, RA as stated below;

Table 5.6: Model Correlation Resistance Component due to Drift Angle, β

AA SCVR 25.0 ρ=

Longitudinal Component Lateral Component

ASLA SCVR 2)( )cos(5.0 βρ= ASTA SCVR 2

)( )sin(5.0 βρ=  

By taking into account and modifying all the related resistance components,

coefficients and functions which influenced by the ship’s velocity due to drift angle,

β, and the additional frictional resistance due to acting current velocity, RF(C) at

various angle, α, the problem of ship resistance prediction with lateral drift effect can

be solved. There are slightly differences with the original procedure, which due to

the presence of ship’s and current velocity component (longitudinal and lateral). The

  59

prediction of ship resistance using the proposed prediction formula can be performed

by solving it separately; longitudinally and laterally.

Applying the original Holtrop’s and Mennen’s prediction approach as the

guideline, it is explored by considering the lateral drift effect due to wind and severe

current. Both of these effects (small drift angle due to wind and severe drift angle

due to current) are calculated separately at each component (longitudinal and lateral).

The modified procedure in determining the total ship resistance, RTotal are written as

follows:

RTotal (longitudinally) = RF (L)’ (1+k) + RAPP + RW + RB + RTR + RA (5.2)

Where RF (L)’= RFS (longitudinal) + RFC (longitudinal) (5.3)

RTotal (lateral) = RF (T)’ (1+k) + RAPP + RW + RB + RTR + RA (5.4)

Where RF (T) ‘= RFS (lateral) + RFC (lateral) (5.5)

RFS = Frictional Resistance due to ship’s velocity, VS

RFC = Frictional Resistance due to current’s velocity, VC

The results of each component are combined in view of trigonometric relationship to

obtain the Total Ship Resistance, RTOTAL with severe drift effects (at various angles).

The proposed trigonometric relation for this Total Ship Resistance, RTOTAL is written

as follows:

RTOTAL= 2)(

2( )()( laterallyTotalallylongitudinTotal RR + (5.6)

CHAPTER VI

COMPUTER PROGRAMMING

6.1 Introduction

At this stage, a calculation programming are essentials due to the

complication of the calculation itself. Therefore, calculation template using

Microsoft Excel and FORTRAN were developed. The results from both calculation

tools will be used for comparison and verification purpose and to further confirm the

correctness of the proposed ship resistance prediciton method.

6.2 Computer Programming Verification

The developed calculation program (FORTRAN) certainly requires to be

verified in order to ensure its validity. The verification of this developed

programming is started upon the source code is written. Stage by stage each of the

derived equation is verified by running the program and comparing the output result

with the result calculated by the Microsoft Excel. Must be borne in mind that in

performing these two mode of calculation, some data is required. In this study, those

61

data are taken similarly with example data provided by Holtrop’s example

calculation (Holtrop J.and Mennen G. G. J.,1982).

6.3 Program Flow Chart

Upon development of this program, the flow chart is produced in visualizing

the flow of this calculation program. The flowchart is available in Appendix A.

6.4 Input and Output Data

As an input, the data in this program is divided into two categories, namely

user input data and data’s set in the programming.

6.4.1 User Input Data

For this particular calculation program, in executing the problem of ship

resistance with lateral drift effect, incorporating the severe case, it requires ship

velocity, VS and current velocity, VC as user input data. These two data are defined as

user input data since they will be the main variables in determining total ship

resistance with lateral drift effect, especially in severe case (due to current).

62

6.4.2 Data in the Programming

This type of data is required and initially is set in the programming. Means,

these data is a fixed and can only be modified or changed by changing the source

code. In performing this particular calculation, main particulars of any proven ships,

are needed, as long as it is within the scopes and limitations of the Holtrop’s and

Mennen’s criteria range. In this case, main particulars data of container ship type is

used, since it is provided by Holtrop’s and Mennen’s example calculation (as

mentioned previously). Apart of the main ship particulars, the main hydrostatics data

of corresponding ship also is required to complete the calculation. Other than that,

properties of water, as a medium for the ship to operate also are necessary data to be

set for the calculation program. The list of data which is set initially in the program

are shown in the Table 6.1.

Table 6.1: List of data’s set in the programming (Holtrop, J. and Mennen, G. G. J.).

MAIN PARTICULARS UNIT Length of Waterline, LWL 205.000 m Breadth Moulded, B 32.000 m Draught Moulded, T 10.000 m Volume displacement, Ñ 37500 m3 Wetted surface Area, S 7381.45 m2 Wetted Surface Area of Appendages, SAPP 50 m2 Prismatic Coeff., CP 0.5833 Midship Area Coeff., CM 0.98 Block Coefficient, CB 0.586 Waterplane. Area Coeff., CWP 0.75 LCB from zero pt. (+ve fwd) -0.75 m Transverse sectional area of bulb, ABT 20 m2 1/2 angle of entrance, iE 12.080 degree Transverse area of immersed transom, AT 16 m2 Centre of bulb area above keel line, hB 4 m Stern shape coefficient, CStern 10.0

Density of salt water, ρSW 1.026 tonne/m3

63

Viscosity of salt water, νSW 1.19-06 m2/s

Gravity Acceleration, g 9.81 m/s2

Drift Angle, β 0-10 deg

Current Direction Angle, α 0-360 deg

6.4.3 Output Data

The output data from this computer programming are listed as follows:

1) Parameters, Coefficients, Functions and Sub- components of Total

Resistance

• Longitudinal Ship Velocity, Vs(L) and Lateral Ship Velocity, Vs(T)

• Longitudinal Current Velocity, Vc(L) and Lateral Current Velocity,

Vc(T)

• Length of run, Lr

• Coefficient of C1, C2, C3, C4, C5, C6(L), C6(T), C7, C12, C13, C15, C16, PB

and CA

• Wetted Surface Area, S

• Reynold Number (longitudinal), Rn(L) and (lateral), Rn(T)

• Frictional Resistance Coefficient, CF, (longitudinal), CF(L) and

(lateral), CF(T)

• Froude’s Number, (Fn), (longitudinal), Fn(L) and (lateral), Fn(T)

• Lambda, λ

• Coefficient of m1, m2, m2(L) and m2(T)

• Immersion Froude’s Number, Fni, (longitudinal), Fni(L) and (lateral),

Fni(T)

• Transom Froude’s Number, Fnt, (longitudinal), Fnt(L) and (lateral),

Fnt(T)

64

2) Total Resistance Components

• Form factor, (1+k)

• Frictional Resistance, RF, (longitudinal), RF(L) and (lateral), RF(T)

• Frictional Resistance (due to current), RFC, (longitudinal), RFC(L) and

(lateral), RFC(T)

• Appendages Resistance, RAPP, (longitudinal), RAPP(L) and (lateral),

RAPP(T)

• Wave- making Resistance, RW, (longitudinal), RW(L) and (lateral), RW(T)

• Bulbous Bow Resistance, RB, (longitudinal), RB(L) and (lateral), RB(T)

• Immersed Transom Resistance, RTR, (longitudinal), RTR(L) and

(lateral), RTR(T)

• Model- Ship Correlation Resistance, RA, (longitudinal), RA(L) and

(lateral), RA(T)

• Resultant Frictional Resistance, RF(Total)

• Resultant Appendages Resistance, RAPP(Total)

• Resultant Wave- making Resistance, RW(Total)

• Resultant Bulbous Bow Resistance, RB (Total)

• Resultant Immersed Transom Resistance, RTR (Total)

• Resultant Model- Ship Correlation Resistance, RA (Total)

3) Final Results

• Total Resistance with Severe Drift Case

CHAPTER VII

 

 

 

 

RESULTS AND DISCUSSION

 

 

7.1. Introduction

Based on the proposed ship resistance prediction formulae that were

discussed in previous chapter and the calculation tools which is based on Microsoft

Excel and FORTRAN, the output results are calculated and analyzed. In this chapter,

it presents and discusses in more detail and wider about the results obtained. Data of

related results are presented effectively in tables and several necessary graphs are

produced to illustrated clearly about the results and related analysis. In this study, the

analysis and discussion also remarks about two case of study as highlighted earlier.

7.2. CASE 1: Severe Drift Effect on the Total Ship Resistance, RTOTAL

As discussed in the earlier chapter, it clearly highlighted that the assumption

of this lateral drift with severe effect are due to two separate elements, wind and

current (maintaining the calm water condition). First effect of lateral drift which

  66

caused by wind is considerably limited up to 10 degrees drift angle, β, assuming

relatively wind effect is small comparing to the forward speed of the ship. However,

as severe lateral drift effect is concerned, it is incorporated with the current cause.

This current is said could give a severe drift effect due to the current velocity (as set

earlier) acts on the moving ship, which considerably gives more severe lateral drift

effect. In measuring wider about this lateral drift effect, the current velocity acting on

the moving ship, especially at river mouth area is varied in term of direction angle.

The current direction angle (with fixed velocity) is represented by α and varies from

0o (also known as heading current) up to 360o, with 10o intervals.

As results, it can be summarized that this lateral drift investigation on the ship

resistance is influenced by two types of variables with fixed values of current

velocity, VC. Consideration is given on the variables from range of drift angles, β, as

well as range of current direction angles, α. The calculated result of the lateral drift

effect on the ship total resistance, RTOTAL is shown in Table 7.1. According to this

result, the total ship resistance is calculated at various drift angles incorporating with

the various current direction angles. The ship’s velocity, VS is set at 25 knots (service

speed) and current velocity, VC is assumed 4 knots (considerably the typical

maximum value). The mathematical calculation for this total ship resistance, RTOTAL

is executed by solving the proposed ship resistance prediction formulae separately

into two components of total ship resistance, namely longitudinally (RT(longitudinal)) and

laterally (RT(lateral)). Both values are then combined by applying the trigonometric

solution as described in previous chapter. These results are plotted and visualized in

Figure 7.1

  67

Table 7.1: CASE 1: Result of Ship Total Resistance with Lateral Drift Effect at

Various Drift and Current Direction Angles

Drift angle, β(deg) 0 2 4 Current direction angle, α

(deg) RTOTAL(L) RTOTAL(T) R (TOTAL) RTOTAL(L) RTOTAL(T) R (TOTAL) RTOTAL(L) RTOTAL(T) R (TOTAL)

0 1824.859 0.000 1824.859 1822.333 2.510 1822.334 1814.751 9.250 1814.774

10 1823.946 1.081 1823.946 1821.420 3.760 1821.424 1813.838 10.499 1813.868

20 1821.308 3.797 1821.311 1818.781 6.900 1818.794 1811.199 13.640 1811.251

30 1817.232 7.692 1817.248 1814.706 11.404 1814.742 1807.124 18.144 1807.215

40 1812.168 12.279 1812.209 1809.642 16.710 1809.719 1802.060 23.449 1802.212

50 1806.675 17.029 1806.755 1804.149 22.203 1804.285 1796.567 28.942 1796.800

60 1801.370 21.408 1801.497 1798.844 27.266 1799.051 1791.262 34.006 1791.585

70 1796.867 24.931 1797.040 1794.341 31.340 1794.615 1786.759 38.080 1787.165

80 1793.728 27.211 1793.935 1791.202 33.977 1791.524 1783.620 40.716 1784.085

90 1792.481 27.998 1792.700 1789.955 34.887 1790.295 1782.373 41.627 1782.859

100 1791.229 27.207 1791.436 1788.703 33.972 1789.025 1781.121 40.712 1781.586

110 1788.086 24.924 1788.260 1785.560 31.332 1785.835 1777.978 38.072 1778.386

120 1783.581 21.399 1783.709 1781.055 27.255 1781.263 1773.473 33.995 1773.799

130 1778.275 17.018 1778.357 1775.749 22.190 1775.888 1768.167 28.930 1768.404

140 1772.782 12.268 1772.825 1770.256 16.697 1770.335 1762.674 23.437 1762.830

150 1767.720 7.681 1767.736 1765.194 11.393 1765.230 1757.612 18.132 1757.705

160 1763.647 3.789 1763.651 1761.121 6.891 1761.135 1753.539 13.631 1753.592

170 1761.013 1.076 1761.013 1758.486 3.754 1758.490 1750.904 10.494 1750.936

180 1760.104 0.000 1760.104 1757.578 2.510 1757.580 1749.996 9.250 1750.020

190 1761.021 1.085 1761.021 1758.495 1.255 1758.495 1750.913 7.995 1750.931

200 1763.663 3.805 1763.667 1761.137 -1.890 1761.138 1753.555 4.850 1753.562

210 1767.741 7.702 1767.758 1765.215 -6.396 1765.227 1757.633 0.343 1757.633

220 1772.807 12.290 1772.850 1770.281 -11.703 1770.320 1762.699 -4.963 1762.706

230 1778.301 17.040 1778.382 1775.775 -17.195 1775.858 1768.193 -10.456 1768.224

240 1783.604 21.417 1783.733 1781.078 -22.257 1781.217 1773.496 -15.518 1773.564

250 1788.105 24.938 1788.278 1785.578 -26.328 1785.773 1777.996 -19.589 1778.104

260 1791.240 27.214 1791.446 1788.714 -28.961 1788.948 1781.132 -22.221 1781.270

270 1792.481 27.998 1792.700 1789.955 -29.867 1790.204 1782.373 -23.128 1782.523

280 1793.739 27.204 1793.945 1791.213 -28.948 1791.447 1783.631 -22.209 1783.769

290 1796.885 24.917 1797.058 1794.359 -26.304 1794.552 1786.777 -19.565 1786.884

300 1801.393 21.389 1801.520 1798.867 -22.225 1799.005 1791.285 -15.485 1791.352

310 1806.700 17.007 1806.780 1804.174 -17.158 1804.256 1796.592 -10.418 1796.622

320 1812.193 12.257 1812.234 1809.667 -11.664 1809.704 1802.085 -4.924 1802.091

330 1817.254 7.671 1817.270 1814.728 -6.361 1814.739 1807.146 0.378 1807.146

340 1821.323 3.781 1821.327 1818.797 -1.862 1818.798 1811.215 4.877 1811.222

350 1823.954 1.071 1823.955 1821.428 1.271 1821.429 1813.846 8.011 1813.864

360 1824.859 0.000 1824.859 1822.333 2.510 1822.334 1814.751 9.250 1814.774

 

 

 

  68

 

Drift angle, β(deg) 6 8 10 Current direction angle, α

(deg) RTOTAL(L) RTOTAL(T) R (TOTAL) RTOTAL(L) RTOTAL(T) R (TOTAL) RTOTAL(L) RTOTAL(T) R (TOTAL)

0 1802.097 19.808 1802.206 1784.332 33.924 1784.655 1761.371 51.370 1762.120

10 1801.184 21.058 1801.307 1783.419 35.173 1783.766 1760.459 52.620 1761.245

20 1798.546 24.198 1798.709 1780.781 38.314 1781.193 1757.820 55.760 1758.704

30 1794.471 28.702 1794.700 1776.706 42.818 1777.222 1753.745 60.264 1754.780

40 1789.406 34.008 1789.729 1771.641 48.123 1772.295 1748.680 65.570 1749.909

50 1783.913 39.501 1784.350 1766.148 53.616 1766.962 1743.187 71.062 1744.635

60 1778.608 44.564 1779.167 1760.843 58.680 1761.821 1737.883 76.126 1739.549

70 1774.106 48.638 1774.772 1756.341 62.754 1757.461 1733.380 80.200 1735.234

80 1770.967 51.275 1771.709 1753.202 65.390 1754.421 1730.241 82.837 1732.223

90 1769.720 52.185 1770.489 1751.955 66.301 1753.209 1728.994 83.747 1731.021

100 1768.467 51.270 1769.210 1750.702 65.386 1751.923 1727.742 82.832 1729.726

110 1765.325 48.630 1765.994 1747.560 62.746 1748.686 1724.599 80.192 1726.462

120 1760.819 44.553 1761.383 1743.054 58.669 1744.042 1720.094 76.115 1721.777

130 1755.514 39.488 1755.958 1737.749 53.604 1738.575 1714.788 71.050 1716.259

140 1750.021 33.995 1750.351 1732.256 48.110 1732.924 1709.295 65.557 1710.552

150 1744.958 28.691 1745.194 1727.193 42.806 1727.723 1704.232 60.253 1705.297

160 1740.886 24.189 1741.054 1723.121 38.305 1723.546 1700.160 55.751 1701.074

170 1738.251 21.052 1738.378 1720.486 35.168 1720.845 1697.525 52.614 1698.340

180 1737.342 19.808 1737.455 1719.577 33.924 1719.912 1696.617 51.370 1697.394

190 1738.259 18.553 1738.358 1720.494 32.668 1720.805 1697.534 50.115 1698.273

200 1740.902 15.408 1740.970 1723.137 29.524 1723.390 1700.176 46.970 1700.824

210 1744.980 10.902 1745.014 1727.215 25.017 1727.396 1704.254 42.464 1704.783

220 1750.046 5.595 1750.055 1732.281 19.711 1732.393 1709.320 37.157 1709.724

230 1755.539 0.103 1755.539 1737.774 14.218 1737.832 1714.813 31.665 1715.106

240 1760.843 -4.959 1760.850 1743.078 9.156 1743.102 1720.117 26.603 1720.323

250 1765.343 -9.030 1765.366 1747.578 5.085 1747.585 1724.617 22.532 1724.764

260 1768.478 -11.663 1768.517 1750.713 2.453 1750.715 1727.752 19.899 1727.867

270 1769.720 -12.569 1769.764 1751.955 1.546 1751.955 1728.994 18.993 1729.098

280 1770.977 -11.650 1771.016 1753.213 2.465 1753.214 1730.252 19.912 1730.366

290 1774.124 -9.006 1774.147 1756.359 5.109 1756.366 1733.398 22.556 1733.545

300 1778.632 -4.927 1778.639 1760.867 9.189 1760.891 1737.906 26.635 1738.110

310 1783.939 0.140 1783.939 1766.174 14.256 1766.231 1743.213 31.702 1743.501

320 1789.431 5.634 1789.440 1771.666 19.749 1771.776 1748.705 37.196 1749.101

330 1794.492 10.937 1794.526 1776.727 25.052 1776.904 1753.766 42.499 1754.281

340 1798.562 15.436 1798.628 1780.797 29.551 1781.042 1757.836 46.998 1758.464

350 1801.193 18.569 1801.289 1783.428 32.684 1783.727 1760.467 50.131 1761.181

360 1802.097 19.808 1802.206 1784.332 33.923 1784.655 1761.371 51.370 1762.120

  69

1500

1550

1600

1650

1700

1750

1800

1850

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Current Angle, a (deg)

Tot

al R

esis

tanc

e,R

TO

TA

L (

kN)

R(t) with 0 deg drift

R(t) with 2 deg drift

R(t) with 4 deg drift

R(t) with 6 deg drift

R(t) with 8 deg drift

R(t) with 10 deg drift

Figure 7.1: CASE 1: Result of Total Ship Resistance with Lateral Drift Effect at

Various Drift and Current Direction Angles

 

Referring to the calculated and analyzed result in Table 7.1 and Figure 7.1, it

is showed that the total ship resistance, RTOTAL incorporating with the effect of lateral

drift decreased with increase of drift angle, β. However, the values of total ship

resistance incorporating with severe drift effect showed decrease trend with the

increase of current direction angle until α = 180o. After 180o, total resistance starts to

increase until current direction angle, α= 360o. From β=0o to 10o and from α=0o to

180o shows that the values of total ship resistance linearly decrease. Must be borne in

mind that this severe drift effect is caused by combination of two types of sources;

due to wind, which produces drift angle, β and due to current, which at its speed of 4

knots (max.) acts at various current direction angle, α.

In discussing more about this effect, we might view the effect of both causes

of severe drift effect separately. In other words, first, we possibly discuss the effect

of lateral drift due wind which causes drift angle, β.

  70

7.2.1 Ship Total Resistance, RTOTAL with the Drift Effect (due to wind)

Appendix B1 shows that the trend of total ship resistance is decrease with the

increase of drift angle, β. The total ship resistance determination at this case is made

by solving it in separate components; longitudinally and laterally. As a result, total

ship resistance is calculated as Longitudinal Total Ship Resistance, RT (L) and Lateral

Total Ship Resistance, RT (T) as shown in Table 7.1. From there, as a resultant of total

ship resistance, it is combined and solved by applying a trigonometric solution.

As indicated in Table 7.2, the total resistance with lateral drift effect due to

drift angle is influenced by component of ship’s velocity parameter, which is ship

longitudinal velocity, VS (L) and ship lateral velocity, VS (T). Due to that, ship

resistance determination is made by breaking down into longitudinal and lateral

component as well, where all the component of resistances, coefficients and

functions are solved separately in longitudinal and lateral direction (as per discussed

in Chapter V). As the result, from the table, it shows that longitudinal total resistance

of the ship, RT(L) decrease with the increase of drift angle, β, whereas in lateral

component, the trend of total resistance, RT(T) is proportionally increase with the

increment of drift angle. It explains that with the increase of drift angle, from β = 0o

to 10o, the resistance acting longitudinally becomes less, but the magnitude increases

in lateral component point of view.

However, we also find out that although the total ship resistance laterally,

RT(T) is proportionally increase, the resultant value of total ship resistance, RTOTAL still

decrease with the increase of drift angle (refer to Table 7.2). This is due to the

increasing values of total resistance in lateral direction, RT (T), which is relatively

small comparing the decreasing values of total resistance in longitudinal component

with the increase of drift angle. This trend are looked similarly with other range of

ship speed values, as shown in Figure 7.2

  71

Table 7.2: Resultant Ship Total Resistance at Speed 25 knots with Various Drift

Angles

 

 

 

 

 

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6 7 8 9 10

Drift Angle,β (deg)

Tota

l Re

sist

ance

, R T (

kN)

Ship speed,v=5 knots ship speed,v=10 knots Ship speed,v=15 knots

Ship speed,v=20 knots Ship speed,v=25 knots Ship speed,v=30 knots

 

Figure 7.2: Total Ship Resistance, RTOTAL at Various Ship Speed, Vs with Lateral Drift Angles (due to wind).

Ship Velocity= 25 knots

Drift angle, β(deg) RTOTAL(L) (kN)

RTOTAL(T) (kN)

R (TOTAL) (kN)

0 1792.48 0.00 1792.48

2 1789.96 2.51 1789.96

4 1782.37 9.25 1782.40

6 1769.72 19.81 1769.83

8 1751.95 33.92 1752.28

10 1728.99 51.37 1729.76

  72

7.2.2 Ship Total Resistance, RTOTAL with Current Effect

On the other hand, besides drift effect due to wind which produces drift

angles, since concerning the severe lateral drift effect at the river mouth, it also is

caused by the current acting on the ship. This factor of lateral drift is said to give

severe effect to the ship, due to the presence of current velocity itself. The

mathematical investigation due to this current speed on the ship resistance is made by

approaching the so called a relative solution. With the fixed value of current velocity,

VC = 4 knots (approx.), the analysis is made by considering various direction of

angles, α. The varying of current direction angles begin at 0o, which also namely as

heading current, with 10o of interval up to 180o (following current), then continues

until α = 360o (which considerably back to heading current). At these various current

direction angles, a wider effect of drift on the ship resistance can be analyzed. For the

analysis of total ship resistance with drift effect only caused by current itself, is

shown in Appendix B2.

In reviewing the total ship resistance at 25 knots with lateral drift due to 4

knots current from point view of longitudinal and lateral component, it shows that

the total ship resistance produced longitudinally, RT(L) decrease with increase of

current direction angle until α = 180o. However, the trend then indicates linearly

increase from α = 190o until reach up to α = 360o (which considerably back to

heading current). There also indicates that the total ship resistance is determined as

maximum value at current direction angles, α= 0o or α = 360o with RT (L) is 1824.86

kN. Whilst, the value of total ship resistance laterally, RT (T) at this angle is zero. This

situation happened since at α= 0o, the current is said in the position of heading

current. Means, the traveled ship at 25 knots is encountered by the current with 4

knots speed completely in longitudinal component and in opposite direction of

traveled ship, and there is absence of lateral component at this direction. Relatively,

at this condition, ship total resistance is added by the resistance produced due to the

heading current at 4 knots and the resistance due to the current is found at highest

value at the α= 0o or α = 360o (heading current).

  73

As passed with the increment of current angle, the longitudinal component of

total resistance starts decreasing, while in lateral component proportionally increase.

This increasing value of lateral component came to the highest point when the

current direction angle, α= 90o, also namely as starboard beam current. The lateral

total resistance, RT (T) is determined 28 kN at this angle. This due to the magnitude of

lateral velocity component at 90o is the maximum magnitude, since there only has the

absolute lateral component, without longitudinal current velocity. This condition also

occurs in the case of port beam current. The only difference is that the total

resistance laterally, RT (T) produced is in the opposite direction of the case of

starboard beam current. After current direction angle passing starboard beam current

(90o), both total resistance produced longitudinally and laterally decrease till

reaching 180o. This trend can be explained that at this range of angle current, the

longitudinal resistance is encountered in opposite direction of current, which is the

same direction with traveled ship. As a result, it is found that the longitudinal

resistance due to current effect is produced in negative values, hence brought the

total ship resistance lesser as compared to the total ship resistance produced in

normal condition. These negative reading of resistance can be interpreted and

converted into the additional force or thrust in moving the ship forward

(longitudinally). The traveled ship is gained a merit in term of powering requirement

at this range of current angles. The peak of this merit was achieved when the current

angle, α at 180o. At this direction (following current) resistance due to this current

produced absolutely in longitudinal component, same direction with the traveled ship

direction. In other words, it produced the maximum value of additional force/ thrust

(negative resistance) for the traveled ship forward. The comprehension of this

various condition of current action in effecting lateral drift is shown in Figure 7.3

below.

 

  74

Figure 7.3: Schematic Diagram of Lateral Drift Effect Due to Current

7.2.3 Ship Total Resistance, RTOTAL with Lateral Drift Effect Due to

Combination of Wind and Current (Severe Case)

In general discussion about total ship resistance produced with the effect of

severe drift; these two causes are combined together. The severe lateral drift due to

combination of wind (due to drift angle) and current (current direction angle), it can

be summarized that the trend is decreased with increase of these angles. In this case,

at ship service speed of 25 knots, the maximum value of total ship resistance

produced is RTOTAL = 1824.86 kN, at the condition when she is encountered by the

heading current (α= 0o or α= 360o) and no drift effect due to wind (β= 0o). Whereas,

the lowest value produced is RTOTAL =1697.39 kN when she is drifted by wind at

maximum drift angle, β= 10o incorporating with the following current (α= 180o). It

is possibly clearer to view the comparison and difference between the total ship

resistance calculated using original Holtrop;s and Mennen’s formula (at normal

X

Vc

Vc(T)

Vc(L)

Y 

Current direction angle Current velocity, Vc

Ship velocity, Vs

α

Up to 360o

  75

condition), with maximum and minimum total ship resistance produced due to the

effect of severe drift (caused by combination of wind and current). The exact values

are shown in Table 7.3

Table 7.3: Comparison of differences between total ship resistance produced in

normal condition with maximum and minimum total ship resistance

produced due to drift effect

Condition at service speed 25 knots Total Resistance,

RTOTAL (kN)

Percentage of

difference

Total ship resistance at normal condition

1792.48

Maximum of total ship resistance produced due to drift effect (caused by combination of wind and current)

1824.86 1.81 %(added)

Minimum of total ship resistance produced due to drift effect (caused by combination of wind and current)

1697.39 5.31 % (reduced)

7.3 Analysis the Effect at Other Ship Velocities

Furthermore, in reviewing the total ship resistance with this drift effect, it

also can be further reviewed at other ship velocities. Result in Table 7.4 (a), (b), (c)

and (d) and graphs in Figure 7.4 (a), (b), (c) and (d) visualized the totals ship

resistance calculated at various ship velocities. It is evaluated by taking into account

the increase of drift angle (β up to 10o) incorporating with current direction angle. On

the whole, the curve of total resistance still follows the ideal trend of total resistance

curve, which increases proportionally when the ship velocity increased. However, in

relating the total ship resistance with drift angles case, the trend of result at other ship

velocities remarkably showed similar with the result discussed earlier, (particularly at

VS = 25 knots). The total ship resistance, R (TOTAL) curves produced at velocity 5, 10,

15, 20 and 30 knots individually decreases with the increase of drift angle, β. The

  76

results specifically are overviewed in four main cases, which is in heading current (α

= 0o), starboard beam current (α = 90o), following current (α = 180o) and port beam

current (α = 270o) and most of them, the total ship resistance produced with the

effect of drift, are decreased when the drift angle is increased.

Table 7.4 (a): Total Ship Resistance Produced Due to Lateral Drift Effect (in

Severe Case) at Various Ship Velocity in Heading Current, α = 0o

Drift angle, β (deg) 0 2 4 6 8 10 Ship Velocity, Vs (knot)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN))

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

0 0.000 0.000 0.000 0.000 0.000 0.000 5 99.27 99.19 98.96 98.59 98.07 97.41 10 273.83 273.57 272.76 271.43 269.60 267.30 15 546.51 545.90 544.06 541.05 536.89 531.67 20 981.20 979.81 975.67 968.91 959.70 948.27 25 1824.86 1822.33 1814.78 1802.21 1784.66 1762.12 30 3025.49 3018.45 2997.52 2963.26 2916.59 2858.74

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30Ship Velocity, Vs (knot)

Total Resistance, RTOTAL (kN)

Drift angle, β (deg) 0Drift angle, β (deg) 2Drift angle, β (deg) 4Drift angle, β (deg) 6Drift angle, β (deg) 8Drift angle, β (deg) 10

Figure 7.4 (a): Total Ship Resistance Curve Produced with Drift Effect (in Severe

Case) at Various Ship Velocity in Heading Current Case, α = 0o

  77

Table 7.4 (b): Total Ship Resistance Produced Due to Lateral Drift Effect (in

Severe Case) at Various Ship Velocity in Starboard Beam Current,

α = 90o

Drift angle, β (deg) 0 2 4 6 8 10 Ship Velocity, Vs (knot)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN))

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

0 0.000 0.000 0.000 0.000 0.000 0.000 5 66.89 74.21 74.24 74.13 73.97 73.76 10 241.45 243.41 242.77 241.71 240.25 238.41 15 514.13 514.10 512.93 510.18 506.39 501.63 20 948.82 948.04 944.06 937.54 928.67 917.67 25 1792.48 1790.29 1782.85 1770.48 1753.10 1731.02 30 2993.11 2986.28 2965.45 2931.36 2884.93 2827.38

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30Ship Velocity, Vs (knot)

Total Resistance, RTOTAL (kN

)

Drift angle, β (deg) 0Drift angle, β (deg) 2Drift angle, β (deg) 4Drift angle, β (deg) 6Drift angle, β (deg) 8Drift angle, β (deg) 10

Figure 7.4 (b): Total Ship Resistance Curve Produced with Drift Effect (in Severe

Case) at Various Ship Velocity in Starboard Beam Current Case, α =

90o

  78

Table 7.4(c): Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe

Case) at Various Ship Velocity in Following Current, α = 180o

Drift angle, β (deg) 0 2 4 6 8 10 Ship Velocity, Vs (knot)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

0 0 0 0 0 0 0 5 34.51 34.43 34.21 33.84 33.34 32.72 10 209.07 208.80 208.00 206.68 204.87 202.59 15 481.75 481.14 479.31 476.30 472.16 466.96 20 916.44 915.05 910.92 904.16 894.96 883.55 25 1760.10 1757.58 1750.02 1737.45 1719.91 1697.39 30 2960.73 2953.69 2932.76 2898.50 2851.83 2794.00

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30Ship Velocity, Vs (knot)

Total Resistance, RTOTAL (kN)

Drift angle, β (deg) 0Drift angle, β (deg) 2Drift angle, β (deg) 4Drift angle, β (deg) 6

Drift angle, β (deg) 8Drift angle, β (deg) 10

Figure 7.4 (c): Total Ship Resistance Curve Produced with Drift Effect (in Severe

Case) at Various Ship Velocity in Following Current Case, α = 180o

  79

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30Ship velocity, Vs (knots)

Total resistance, RTOTAL (kN)

Drift angle, β (deg) 0Drift angle, β (deg) 2Drift angle, β (deg) 4Drift angle, β (deg) 6Drift angle, β (deg) 8Drift angle, β (deg) 10

Table 7.4 (d): Total Ship Resistance Produced Due to Lateral Drift Effect (in

Severe Case) at Various Ship Velocity in Port Beam Current, α =

270o

 

Figure 7.4 (d): Total Ship Resistance Curve Produced with Drift Effect (in

Severe Case) at Various Ship Velocity in Port Beam Current

Case, α = 270o

 

 

 

 

Drift angle, β (deg) 0 2 4 6 8 10 Ship Velocity, Vs (knot)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

R (TOTAL) (kN)

0 0 0 0 0 0 0 5 66.89 74.19 73.84 73.28 72.51 71.54 10 241.45 243.28 242.33 240.76 238.61 235.90 15 514.13 514.47 512.48 509.22 504.73 499.08 20 948.82 947.92 943.64 936.64 927.11 915.28 25 1792.48 1790.20 1782.52 1769.76 1751.95 1729.09 30 2993.11 2986.20 2965.17 2930.75 2883.85 2825.72

  80

7.4 CASE 2: Severe Drift Effect on the Total Ship Resistance, RTOTAL

 

 

The total ship resistance in Case 2 is solved and approached similarly as in

Case 1 which treated as resultant of longitudinal and lateral component. Comparing

to the Case 1, based on the methodology, the values of total resistance is totally

depend on the lateral resistance component, since the longitudinal resistance values

is similar with the values in Case 1. So that, in this particular section, the discussion

is focused more on the result of total resistance in lateral direction. The difference in

Case 2 is that, besides the effect of ship velocity, VS the other main modified

parameters including ship length and breadth as well.

Referring to the Table 7.5, it is indicated that the values of total resistance

(laterally), RT (L) is remarkably large in comparison to the values in Case 1. However,

from point view of lateral total resistance, it still follows the trend in Case 1. The

obvious difference is about the values obtained. Comparing to the Case 1, in Case 2,

the lateral total resistance calculated gave a drastic increase. Even though with the

same trend, the values obtained are very big in comparison to Case 1. Taking one

point as an example, when the ship is drifted at β = 10 degrees incorporating with the

current direction angle, α = 90 degrees, it is obtained that the lateral total resistance,

RT (L) is 828.03 kN for the Case 2. If compared to the Case 1, the lateral total

resistance produced at this point is just about 83.75. kN. In comparison these two

values, which is taken at maximum point, the lateral total resistance determined at

Case 2 almost 43.19% of total ship resistance (resultant of total resistance). Whereas,

the percentage of the maximum lateral total resistance obtained in Case 1 is

only.4.84% of the resultant of total resistance.. Figure 7.5 and Figure 7.6 illustrated

clearer about the comparison between Case 1 and Case 2, as far as lateral total

resistance is concerned. In overall, the large differences of lateral total resistance

obtained between Case1 and 2 might be due to some assumptions decided earlier,

which possibly could contribute to the error. One of reason, maybe due to the

unsymmetrical form of ship in Case 2. By changing inversely the length and breadth,

it created the form of ship unsymmetrical. Obviously the solution of this

unsymmetrical condition is a complicated problem to be executed.

  81

Table 7.5: CASE 2: Longitudinal, Lateral and Resultant Total Resistance at

Various Current Direction Angle and Drift Angle.

Drift angle, β(deg)

0 2 4

Current direction angle, α

(deg) RT (L) RT (T)

R (TOTAL) RT (L) RT (T)

R (TOTAL) RT (L) RT (T)

R (TOTAL)

0 1824.86 0.00 1824.86 1822.33 23.61 1822.49 1814.75 84.31 1816.71

10 1823.95 15.00 1824.01 1821.42 38.61 1821.83 1813.84 99.31 1816.55

20 1821.31 51.88 1822.05 1818.78 75.49 1820.35 1811.20 136.19 1816.31

30 1817.23 104.26 1820.22 1814.71 127.87 1819.21 1807.12 188.57 1816.94

40 1812.17 165.61 1819.72 1809.64 189.22 1819.51 1802.06 249.92 1819.31

50 1806.67 228.89 1821.12 1804.15 252.50 1821.73 1796.57 313.20 1823.66

60 1801.37 287.07 1824.10 1798.84 310.67 1825.47 1791.26 371.38 1829.35

70 1796.87 333.79 1827.61 1794.34 357.40 1829.59 1786.76 418.10 1835.02

80 1793.73 364.00 1830.29 1791.20 387.61 1832.66 1783.62 448.31 1839.10

90 1792.48 374.43 1831.17 1789.96 398.03 1833.68 1782.37 458.73 1840.46

100 1791.23 363.95 1827.83 1788.70 387.56 1830.21 1781.12 448.26 1836.66

110 1788.09 333.70 1818.96 1785.56 357.31 1820.96 1777.98 418.01 1826.46

120 1783.58 286.94 1806.52 1781.05 310.55 1807.93 1773.47 371.25 1811.91

130 1778.28 228.74 1792.93 1775.75 252.35 1793.59 1768.17 313.05 1795.67

140 1772.78 165.46 1780.49 1770.26 189.07 1780.32 1762.67 249.77 1780.28

150 1767.72 104.13 1770.78 1765.19 127.74 1769.81 1757.61 188.44 1767.68

160 1763.65 51.78 1764.41 1761.12 75.38 1762.73 1753.54 136.08 1758.81

170 1761.01 14.94 1761.08 1758.49 38.54 1758.91 1750.90 99.24 1753.71

180 1760.10 0.00 1760.10 1757.58 23.61 1757.74 1750.00 84.31 1752.03

190 1761.02 -15.06 1761.09 1758.49 8.54 1758.52 1750.91 69.25 1752.28

200 1763.66 -51.99 1764.43 1761.14 -28.38 1761.37 1753.56 32.32 1753.85

210 1767.74 -104.40 1770.82 1765.22 -80.79 1767.06 1757.63 -20.09 1757.75

220 1772.81 -165.76 1780.54 1770.28 -142.15 1775.98 1762.70 -81.45 1764.58

230 1778.30 -229.03 1792.99 1775.77 -205.43 1787.62 1768.19 -144.72 1774.11

240 1783.60 -287.19 1806.58 1781.08 -263.59 1800.48 1773.50 -202.88 1785.06

250 1788.10 -333.88 1819.01 1785.58 -310.28 1812.34 1778.00 -249.58 1795.43

260 1791.24 -364.05 1827.86 1788.71 -340.44 1820.82 1781.13 -279.74 1802.97

270 1792.48 -374.43 1831.17 1789.96 -350.82 1824.01 1782.37 -290.12 1805.83

280 1793.74 -363.90 1830.28 1791.21 -340.30 1823.25 1783.63 -279.59 1805.41

290 1796.89 -333.61 1827.59 1794.36 -310.00 1820.94 1786.78 -249.30 1804.09

300 1801.39 -286.82 1824.08 1798.87 -263.21 1818.02 1791.29 -202.51 1802.70

310 1806.70 -228.60 1821.11 1804.17 -204.99 1815.78 1796.59 -144.29 1802.38

320 1812.19 -165.32 1819.72 1809.67 -141.71 1815.21 1802.08 -81.01 1803.90

330 1817.25 -103.99 1820.23 1814.73 -80.39 1816.51 1807.15 -19.69 1807.25

340 1821.32 -51.67 1822.06 1818.80 -28.06 1819.01 1811.22 32.64 1811.51

350 1823.95 -14.87 1824.01 1821.43 8.73 1821.45 1813.85 69.44 1815.17

360 1824.86 0.00 1824.86 1822.33 23.61 1822.49 1814.75 84.31 1816.71

  82

Drift angle, β(deg)

6 8 10

Current direction

angle, α (deg)

RT(L) RT (T) R

(TOTAL) RT (L) RT (T) R

(TOTAL) RT (L) RT (T) R

(TOTAL) 0 1802.10 177.70 1810.84 1784.33 301.42 1809.61 1761.37 453.60 1818.84

10 1801.18 192.70 1811.46 1783.42 316.42 1811.27 1760.46 468.60 1821.76

20 1798.55 229.58 1813.14 1780.78 353.30 1815.49 1757.82 505.48 1829.06

30 1794.47 281.97 1816.49 1776.71 405.68 1822.43 1753.74 557.87 1840.34

40 1789.41 343.32 1822.04 1771.64 467.03 1832.17 1748.68 619.21 1855.08

50 1783.91 406.59 1829.66 1766.15 530.31 1844.05 1743.19 682.49 1872.03

60 1778.61 464.77 1838.33 1760.84 588.49 1856.58 1737.88 740.67 1889.13

70 1774.11 511.50 1846.37 1756.34 635.21 1867.68 1733.38 787.39 1903.84

80 1770.97 541.70 1851.96 1753.20 665.42 1875.23 1730.24 817.60 1913.69

90 1769.72 552.13 1853.85 1751.95 675.85 1877.79 1728.99 828.03 1917.04

100 1768.47 541.65 1849.56 1750.70 665.37 1872.88 1727.74 817.55 1911.41

110 1765.32 511.40 1837.91 1747.56 635.12 1859.39 1724.60 787.30 1895.81

120 1760.82 464.65 1821.09 1743.05 588.36 1839.68 1720.09 740.54 1872.73

130 1755.51 406.45 1801.95 1737.75 530.16 1816.82 1714.79 682.35 1845.56

140 1750.02 343.17 1783.35 1732.26 466.88 1794.07 1709.29 619.07 1817.95

150 1744.96 281.83 1767.57 1727.19 405.55 1774.17 1704.23 557.73 1793.17

160 1740.89 229.48 1755.94 1723.12 353.20 1758.95 1700.16 505.38 1773.68

170 1738.25 192.64 1748.89 1720.49 316.36 1749.33 1697.53 468.54 1761.00

180 1737.34 177.70 1746.41 1719.58 301.42 1745.80 1696.62 453.60 1756.21

190 1738.26 162.64 1745.85 1720.49 286.36 1744.16 1697.53 438.54 1753.26

200 1740.90 125.71 1745.43 1723.14 249.43 1741.10 1700.18 401.61 1746.97

210 1744.98 73.30 1746.52 1727.21 197.02 1738.42 1704.25 349.20 1739.66

220 1750.05 11.94 1750.09 1732.28 135.66 1737.58 1709.32 287.84 1733.39

230 1755.54 -51.33 1756.29 1737.77 72.39 1739.28 1714.81 224.57 1729.46

240 1760.84 -109.49 1764.24 1743.08 14.23 1743.14 1720.12 166.41 1728.15

250 1765.34 -156.18 1772.24 1747.58 -32.46 1747.88 1724.62 119.72 1728.77

260 1768.48 -186.34 1778.27 1750.71 -62.63 1751.83 1727.75 89.55 1730.07

270 1769.72 -196.72 1780.62 1751.95 -73.01 1753.48 1728.99 79.18 1730.81

280 1770.98 -186.20 1780.74 1753.21 -62.48 1754.33 1730.25 89.70 1732.58

290 1774.12 -155.91 1780.96 1756.36 -32.19 1756.65 1733.40 119.99 1737.55

300 1778.63 -109.12 1781.98 1760.87 14.60 1760.93 1737.91 166.78 1745.89

310 1783.94 -50.90 1784.66 1766.17 72.82 1767.67 1743.21 225.00 1757.67

320 1789.43 12.39 1789.47 1771.67 136.10 1776.89 1748.71 288.28 1772.31

330 1794.49 73.71 1796.01 1776.73 197.43 1787.66 1753.77 349.61 1788.27

340 1798.56 126.03 1802.97 1780.80 249.75 1798.23 1757.84 401.93 1803.20

350 1801.19 162.83 1808.54 1783.43 286.55 1806.30 1760.47 438.73 1814.31

360 1802.10 177.70 1810.84 1784.33 301.42 1809.61 1761.37 453.60 1818.84

  83

Figure 7.5: CASE 1: Lateral Total Resistance, RT (T) at Various Current

Direction Angle, α and Various Drift Angle, β (at speed 25 knots)

Current Angle, α

RT (T)

  84

Figure7.6: CASE 2: Lateral Total Resistance, RT (T) at Various Current

Direction Angle, α and Various Drift Angle, β (at speed 25 knots)

On the whole, even though the longitudinal total resistance, RT (L) values

similar with Case 1, with the remarkable values of total resistance (laterally), RT(L)

produced in Case 2, it consequently will reflect the resultant total resistance, RTOTAL.

Due to that, the end result of total ship resistance (applying the described

methodology) gave a certain difference between Case 1 and Case 2, where the result

for the Case 1 is significantly higher. It considerably can be concluded that the result

obtained in Case 1 is preferable and more acceptable. It is said so since the values of

lateral total resistance obtained in Case 2 were too large at every current angle.

Referring to the Figure 7.6, the maximum lateral total resistance obtained is at drift

angle, β = 10 degrees with the current experienced at α = 90. At this point, the values

is up to 828.027 kN, which approaching almost half of the longitudinal total

resistance, and considerably a large value. The values in this lateral component

preferably should not be at this range because the ship has a forward velocity, which

definitely contribute the major influence in total resistance. Other than that, although

it is said as severe lateral drift due to the combination of wind and current, in the

Current Angle, α

RT (T)

  85

assumption of no effects of waves, there is not possible to the values obtained up to

this range. In fact, although in the condition of extreme sea, the influence is still

small because the main effect is come from ocean waves.

 

CHAPTER VIII

CONCLUDING REMARKS

8.1 Conclusion

On the whole, concerning about the earlier objectives of this research, it can

be summarized that they are successfully achieved. As far as this preliminary study is

concerned, base on the literature reviewed, the mathematical derived and calculated

results, this research potentially could contribute significant differences in certain

condition in this ship resistance study. In this particular study, with specific case of

severe lateral drift, instead of existing ship resistance prediction formulas, it is

viewed that more detail and specific value can be calculated and predicted.

Although the condition of severe lateral drift effect due to wind and current is

not entirely experienced by the ship in actual operation, but for a specific case of

river mouth area (as discussed on the earlier part), it also can be considered that the

predicted value would be more practical for a ship which travelling in this case. It is

viewed that this matter is practical especially in ship operations which economy issue

become the priority. This is because determining engine power requirement correctly

at this particular condition will determine the correct fuel consumption for the engine

to be used. As discussed in the previous chapter, in certain case (Case 1) such as

88

when ship traveled at her service speed (25 knots) with drift angle (β = 0 deg) in

heading current (α = 0 deg), it produced the maximum of total ship resistance

(RTOTAL = 1824.86 kN). This can be interpreted that about 1.806 % of total ship

resistance is added in comparison to the normal condition of operation (with no drift

effect). Another case is when ship is experienced a maximum drift angle (β = 10 deg)

and traveled in following current, the total resistance produced is reduced up to 5.305

% of total ship resistance. Meaning, there exists an additional thrust or force for the

ship when operating at this specific condition.

As far as the first initiative of research is concerned in this study, an

investigation which is made by using Holtrop’s and Mennen’s prediction formulae as

a guideline and main basis is considerably promising. A few information and

understanding about this complicated problem are gained in initiating more detail

studies in the near future. Some argument possibly will arise here regarding the

principle used in this problem determination, since Holtrop’s approach is

considerably a statistical method. However, it is highlighted that, at earlier of the

Holtrop’s finding, an attempt also was made to extend the method by adjusting the

original numerical prediction model to test data obtained in specific case, because the

accuracy of the method was reported to be insufficient when unconventional

combination of main parameters were used. Due to this adaption of the method has

resulted this set of Holtrop’s formulae with a wider range of application (Holtrop and

Mennen, 1982).

8.2 Recommendation for Future Research

Lastly, it is viewed that there have a large rooms of research opportunity

possibly be explored and studied for the next stage of investigation. This initial

investigation possibly can be made onto other methods of ship resistance prediction,

as well as another types of ships and hull forms. Besides, as the future research, more

89

study is needed and developed especially for strong verification of this initial

investigation. In this nearer period of time, computer simulation approach, such as

Computer Fluid Dynamics (CFD) could provide a better promising result in solving

the lateral drift effect onto ship resistance. Other than that, a specific model

experiment is seen one of the approaches that possibly to be focused in the near

future, which can further verify the proposed ship resistance prediction formulae.

REFERENCES

Arizam, A. W. (2003) “ Resistance Prediction of the Tugboat” Undergraduate

Thesis. University Technology Malaysia, Skudai

Bertram, V. (2000). Practical Ship Hydrodynamics. Butterworth- Heinemann.

Linacre House, Jordan Hill, Oxford.

Carlton, J. S. (1994). Marine Propellers and Propulsion. Butterworth-

Heinemann. Linacre House, Jordan Hill, Oxford.

Takao I. (1962). Wave – Making Resistance of Ships. The Society of Naval

Architects and Marine Engineers, 70. pg 283-353.

Edward, V. L. (1988). Principles of Naval Architecture, Volume II. Resistance,

Propulsion and Vibration. Jersey City, NJ: The Society of Naval

Architectures and Marine Engineers.

Faizul A. A. (1996). A Study of Ship Resistance Prediction Method.

Undergraduate Thesis. University Technology Malaysia, Skudai.

Faizul A. A, (2006). A Strip Method for a Laterally Drifting Ship in Waves. Ph.D

Thesis. Hiroshima University, Japan.

Faizul A. A. and Yasukawa, H. (2007). Strip Method for a Laterally Drifting ship

in Waves. J Mar Sci Technol. 12: 139–149

90

Gillmer, C and Johson, B. (1982). Introduction to Naval Architecture. London: E.

& F. N. Spon Ltd.

Harold, E. S. (1957). Hydrodynamics in Ship Design. (Vol III). New York: The

Society of Naval Architectures and Marine Engineers.

Harvald, S. V. (1983). Resistance and Propulsion of Ships. Lyngby, Denmark:

John Wiley & Sons.

Holtrop, J. and Mennen, G. G. J. (1982). An Approximate Power Prediction

Method. Netherlands Ship Model Basin, (Marin), Netherland

Holtrop, J. (1984), A Statistical Re-Analysis of Resistance and Propulsion Data.

International Shipbuilding Progress, Vol. 31, No. 363,

Iwasaka, N. and K. Hanawa (1990). Climatologies of marine meteorological

variables and surface fluxes in the North Pacific computed from COADS.

Tohoku Geophys. J., 33, 188–239.

Longo, J. and Stern, F. (2001). Effects of Drift Angle on Model Ship Flow.

University of Iowa, USA

Tupper, E.C. (1996). Introduction to Naval Architecture. (3rd ed.) Formerly

Muckle’s Naval Architecture for Marine Engineers.

APPENDIX A1

Flowchart of Computer Programming to Calculate the Longitudinal Total

Resistance with Drift Effect.

START

Ship Velocity, VsCurrent velocity, Vc

Cstern=10 C13 = 1 + 0.003*Cstern

x1 = (1-Cp+0.0225*LCB)**0.6906 k1 = C13*(0.93+(C12*(B/

Lr)**0.92497*(0.95-Cp)**(-0.521448)*x1))

Beta = Angle*3.142/180Alfa = Angle_2*3.142/180

V = V*cos(Beta)Vc = ABS(Vc*cos(Alfa))

Rn = V*L/Visc Rnc = Vc*L/Visc

Cf = 0.075/(ALOG10(Rn)-2)**2Cfc = 0.075/(ALOG10(Rnc)-2)**2

RFs = 0.5*rho*S*(V**2)*CfRFc = 0.5*rho*S*(Vc**2)*Cfc

RFL = RFs + RFc

IF (B/L .GT. 0.25)

C7 = (B/L)

C7 = 0.5-0.0625*(L/B)

x5=(Lr/B)**0.34574*(100*Vdisp/L**3)**0.16302

x4=-(L/B)**0.80855*(1-Cwp)**0.30484*(1-Cp-

0.0225*LCB)**0.6367*x5 ie = 1+89*EXP(x4)

C1= 2223105*(C7**3.78613)*(T/B)**1.07961*(90-ie)**(-1.37565)

x6 = B*T*(0.31*Abt**0.5+Tf-Hb) C3 = 0.56*Abt**1.5/x6

C2 = EXP(-1.89*C3**0.5)C5 =1-(0.8*At)/(B*T*Cm) Fn = V/(gvt*L)**0.5

IF (L/B .GT. 12)

Lamda = 1.446*Cp-0.36

Cont A

true

false

Cp = 0.5833 LCB = -0.75

L = 205T = 10B = 32

Cb = 0.5860 Cm = 0.98 Cwp = 0.75

Abt = 20 rho = 1.025

V = Speed*0.5144 Vc = Speed_c*0.5144 Visc = 0.0000011906

S = 7381.45Sapp = 50

Vdisp = 37500 Tf = 10 Hb = 4At = 16

gvt = 9.81 Lr = (1-Cp+(0.06*Cp*LCB)/

(4*Cp-1))*L

If(T/L .GT. 0.05)

C12 = (T/L)**0.2228446

IF (0.02 .LT. T/L .AND. T/L .LT. 0.05)

C12 = 48.20*(T/L-0.02)**2.078 + 0.479948

true

else

C12 = (T/L)**0.2228446

IF (90 .GE. Angle_2 .AND. Angle_2 .LE.270)

RFL = RFs - RFc

k2 = 1.5 k2eq = k2*Sapp/Sapp

RAPPL = 0.5*rho*(V**2)*Sapp*K2eq*Cf

true

Cont A

IF (0.11 .LT. B/L .AND. B/L .LT. 0.25)

true

else

C7 = 0.229577*(B/L)**0.33333

else

Lamda = 1.446*Cp-0.03*L/B

true

else

IF (Cp .GT. 0.8)

C16 = 1.73014-0.7067*Cp

true

C16 = 8.07981*Cp-13.8673*Cp**2+6.98

4388*Cp**3

m1=0.0140407*L/T-(1.75254*Vdisp**(0.33333)/L)-

(4.79323*B/L)-C16

IF (L**3/Vdisp .GT. 1727)

C15 = 0

else

else

true

IF (L**3/Vdisp .GT. 1727)

C15 = -1.69385+(L/Vdisp**0.66667-8)/2.36

C15 = -1.69385

m2 = C15*Cp**2*EXP(-0.1*Fn**(-2)) x3 = m1*Fn**(-0.9)+m2*cos(Lamda*Fn**(-2))

RWL = C1*C2*C5*Vdisp*rho*gvt*EXP(x3)

else true

Cont B

10

else

true

IF (270 .GE. Angle_2 .AND.

Angle_2 .LE.360)

else

true

APPENDIX A1

Flowchart of Computer Programming to Calculate the Longitudinal Total

Resistance with Drift Effect.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cont B

x7 = gvt*(Tf-Hb-0.25*(Abt**0.5))+0.15*V**2 Fni = V/x7**0.5

Pb = (0.56*Abt**0.5)/(Tf-1.5*Hb) RBL = (0.11*EXP(-3*Pb**(-

2))*Fni**3*Abt**1.5*rho*gvt)/(1+Fni**2)

Fnt = V/(2*gvt*At/(B+B*Cwp))**0.5

IF (Fnt .LT. 5)

C6 = 0.2*(1-0.2*Fnt) C6 = 0

else

true

RTRL = 0.5*rho*V**2*At*C6

IF (Tf/L .GT. 0.04)

C4 = Tf/L C4 = 0.04

elsetrue

x8 = 0.003*(L/7.5)**0.5*Cb**4*C2*(0.04-

C4)Ca = 0.006*(L+100)**(-

0.16)-0.00205+x8RAL = 0.5*rho*V**2*S*Ca

RTL = RFL*(k1) + RAPPL + RWL + RBL + RTRL + RAL

Drift Angle Value <= 8

Angle = Angle +2

Current Angle_2 <=350

Angle_2 = Angle_2 +10

END

10

true

true

else

else

APPENDIX A2

Flowchart of Computer Programming to Calculate the Lateral Total Resistance

with Drift Effect.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

START

Ship Velocity, VsCurrent velocity, Vc

Cstern=10 C13 = 1 + 0.003*Cstern

x1 = (1-Cp+0.0225*LCB)**0.6906 k1 = C13*(0.93+(C12*(B/

Lr)**0.92497*(0.95-Cp)**(-0.521448)*x1))

Beta = Angle*3.142/180Alfa = Angle_2*3.142/180

V = V*sin(Beta)Vc = ABS(Vc*sin(Alfa))

Rn = V*L/Visc Rnc = Vc*L/Visc

Cf = 0.075/(ALOG10(Rn)-2)**2Cfc = 0.075/(ALOG10(Rnc)-2)**2

RFs = 0.5*rho*S*(V**2)*CfRFc = 0.5*rho*S*(Vc**2)*Cfc

RFT = RFs + RFc

IF (B/L .GT. 0.25)

C7 = (B/L)

C7 = 0.5-0.0625*(L/B)

x5=(Lr/B)**0.34574*(100*Vdisp/L**3)**0.16302

x4=-(L/B)**0.80855*(1-Cwp)**0.30484*(1-Cp-

0.0225*LCB)**0.6367*x5 ie = 1+89*EXP(x4)

C1= 2223105*(C7**3.78613)*(T/B)**1.07961*(90-ie)**(-1.37565)

x6 = B*T*(0.31*Abt**0.5+Tf-Hb) C3 = 0.56*Abt**1.5/x6

C2 = EXP(-1.89*C3**0.5)C5 =1-(0.8*At)/(B*T*Cm) Fn = V/(gvt*L)**0.5

IF (L/B .GT. 12)

Lamda = 1.446*Cp-0.36

Cont A

true

false

Cp = 0.5833 LCB = -0.75

L = 205T = 10B = 32

Cb = 0.5860 Cm = 0.98 Cwp = 0.75

Abt = 20 rho = 1.025

V = Speed*0.5144 Vc = Speed_c*0.5144 Visc = 0.0000011906

S = 7381.45Sapp = 50

Vdisp = 37500 Tf = 10 Hb = 4At = 16

gvt = 9.81 Lr = (1-Cp+(0.06*Cp*LCB)/

(4*Cp-1))*L

If(T/L .GT. 0.05)

C12 = (T/L)**0.2228446

IF (0.02 .LT. T/L .AND. T/L .LT. 0.05)

C12 = 48.20*(T/L-0.02)**2.078 + 0.479948

true

else

C12 = (T/L)**0.2228446

IF (180 .GE. Angle_2 .AND. Angle_2 .LE.360)

RFT = RFs - RFc

k2 = 1.5 k2eq = k2*Sapp/Sapp

RAPPT = 0.5*rho*(V**2)*Sapp*K2eq*Cf

true

Cont A

IF (0.11 .LT. B/L .AND. B/L .LT. 0.25)

true

else

C7 = 0.229577*(B/L)**0.33333

else

Lamda = 1.446*Cp-0.03*L/B

true

else

IF (Cp .GT. 0.8)

C16 = 1.73014-0.7067*Cp

true

C16 = 8.07981*Cp-13.8673*Cp**2+6.98

4388*Cp**3

m1=0.0140407*L/T-(1.75254*Vdisp**(0.33333)/L)-

(4.79323*B/L)-C16

IF (L**3/Vdisp .GT. 1727)

C15 = 0

else

else

true

IF (L**3/Vdisp .GT. 1727)

C15 = -1.69385+(L/Vdisp**0.66667-8)/2.36

C15 = -1.69385

m2 = C15*Cp**2*EXP(-0.1*Fn**(-2)) x3 = m1*Fn**(-0.9)+m2*cos(Lamda*Fn**(-2))

RWT = C1*C2*C5*Vdisp*rho*gvt*EXP(x3)

else true

Cont B

10

else

true

APPENDIX A2

Flowchart of Computer Programming to Calculate the Lateral Total Resistance

with Drift Effect.

 

 

 

Cont B

x7 = gvt*(Tf-Hb-0.25*(Abt**0.5))+0.15*V**2 Fni = V/x7**0.5

Pb = (0.56*Abt**0.5)/(Tf-1.5*Hb) RBT = (0.11*EXP(-3*Pb**(-

2))*Fni**3*Abt**1.5*rho*gvt)/(1+Fni**2)

Fnt = V/(2*gvt*At/(B+B*Cwp))**0.5

IF (Fnt .LT. 5)

C6 = 0.2*(1-0.2*Fnt) C6 = 0

else

true

RTRT = 0.5*rho*V**2*At*C6

IF (Tf/L .GT. 0.04)

C4 = Tf/L C4 = 0.04

elsetrue

x8 = 0.003*(L/7.5)**0.5*Cb**4*C2*(0.04-

C4)Ca = 0.006*(L+100)**(-

0.16)-0.00205+x8RAT = 0.5*rho*V**2*S*Ca

RTT = RFT*(k1) + RAPPT + RWT + RBT + RTRT + RAT

Drift Angle Value <= 8

Angle = Angle +2

Current Angle_2 <=350

Angle_2 = Angle_2 +10

END

10

true

true

else

else

 

APPENDIX B1: Total Ship Resistance, RT Determination in Longitudinal and Lateral Component with Drift Effect Caused by Drift Angle, β (due to wind)

Ship Speed, V(knot) 25

Ship Speed, V(m/s) 12.86

Fn 0.286767239

Longitudinal Component

Drift angle, β(deg) Longi. Ship

Speed, VL(m/s) Fn(L) RF m2 RW FnT C6 RTR RAPP Fni RB CA RA RTOTAL(L)

0 12.86000 0.28677 869.62581 -0.170823598 557.2074 5.4316 0.00 0.00 8.8359 1.50826 0.0492 3.52E-04 220.7493 1792.4813

2 12.85216 0.28659 868.62892 -0.170570408 556.1132 5.4283 0.00 0.00 8.8258 1.50766 0.0492 3.52E-04 220.4803 1789.9552

4 12.82867 0.28607 865.64271 -0.169810624 552.8204 5.4183 0.00 0.00 8.7955 1.50584 0.0491 3.52E-04 219.6748 1782.3732

6 12.78953 0.28520 860.68048 -0.168543633 547.2940 5.4018 0.00 0.00 8.7450 1.50280 0.0490 3.52E-04 218.3367 1769.7198

8 12.73481 0.28398 853.76434 -0.166768499 539.4617 5.3787 0.00 0.00 8.6748 1.49854 0.0487 3.52E-04 216.4724 1751.9548

10 12.66458 0.28241 844.92512 -0.164484096 529.1939 5.3490 0.00 0.00 8.5850 1.49304 0.0484 3.52E-04 214.0912 1728.9939

Lateral Component

Drift angle, β(deg) Lateral Ship

Speed, VT(m/s) Fn(T) RF m2 RW FnT C6 RTR RAPP Fni RB CA RA RTOTAL(L)

0 0.00000 0.00000 0.00000 0 0.0000 0.0000 0.20000 0.0000 0.0000 0.00000 0.0000 0.0003525 0.0000 0.0000

2 0.44887 0.01001 1.64827 0 0.0000 0.1896 0.19242 0.3182 0.0167 0.06484 0.0000 0.0003525 0.2689 2.5100

4 0.89718 0.02001 5.96096 -1.8078E-109 0.0000 0.3789 0.18484 1.2212 0.0606 0.12948 0.0001 0.0003525 1.0744 9.2496

6 1.34441 0.02998 12.65676 -2.74644E-49 0.0000 0.5678 0.17729 2.6301 0.1286 0.19372 0.0003 0.0003525 2.4126 19.8080

8 1.79000 0.03992 21.58593 -3.17767E-28 0.0000 0.7560 0.16976 4.4645 0.2193 0.25737 0.0008 0.0003525 4.2768 33.9235

10 2.23340 0.04980 32.63145 -1.7831E-18 0.0000 0.9433 0.16227 6.6436 0.3316 0.32024 0.0014 0.0003525 6.6581 51.3698  

 

APPENDIX B2: Total Ship Resistance at Service Speed 25 Knots with Lateral Drift Effect due to Current (4 knots)at Various Current Direction Angles.

Ship Speed, v(knot) 25 Fn 0.287

Current speed, VC(knot) 4

Current Direction, a Ship

Speed, v(m/s)

Current speed, Vc component

RF (due to current)

component RTOTAL (due to current effect)

VC(L) VC(T) RF RFC(L) RFC(T) RW RTR RAPP RB RA RTOTAL(L) RTOTAL(T) RTOTAL 0.00001 12.860 4.000 0.000 869.626 27.998 0.000 557.207 0.000 8.836 0.049 220.749 1824.859 0.000 1824.859

10 12.860 3.939 0.695 869.626 27.209 1.081 557.207 0.000 8.836 0.049 220.749 1823.946 1.081 1823.946 20 12.860 3.759 1.368 869.626 24.927 3.797 557.207 0.000 8.836 0.049 220.749 1821.308 3.797 1821.311 30 12.860 3.464 2.000 869.626 21.403 7.692 557.207 0.000 8.836 0.049 220.749 1817.232 7.692 1817.248 40 12.860 3.064 2.571 869.626 17.024 12.279 557.207 0.000 8.836 0.049 220.749 1812.168 12.279 1812.209 50 12.860 2.571 3.064 869.626 12.274 17.029 557.207 0.000 8.836 0.049 220.749 1806.675 17.029 1806.755 60 12.860 2.000 3.464 869.626 7.686 21.408 557.207 0.000 8.836 0.049 220.749 1801.370 21.408 1801.497 70 12.860 1.367 3.759 869.626 3.793 24.931 557.207 0.000 8.836 0.049 220.749 1796.867 24.931 1797.040 80 12.860 0.694 3.939 869.626 1.078 27.211 557.207 0.000 8.836 0.049 220.749 1793.728 27.211 1793.935 90 12.860 0.001 4.000 869.626 0.000 27.998 557.207 0.000 8.836 0.049 220.749 1792.481 27.998 1792.700

100 12.860 0.695 3.939 869.626 1.083 27.207 557.207 0.000 8.836 0.049 220.749 1791.229 27.207 1791.436 110 12.860 1.369 3.758 869.626 3.801 24.924 557.207 0.000 8.836 0.049 220.749 1788.086 24.924 1788.260 120 12.860 2.001 3.464 869.626 7.697 21.399 557.207 0.000 8.836 0.049 220.749 1783.581 21.399 1783.709 130 12.860 2.572 3.063 869.626 12.285 17.018 557.207 0.000 8.836 0.049 220.749 1778.275 17.018 1778.357 140 12.860 3.065 2.570 869.626 17.035 12.268 557.207 0.000 8.836 0.049 220.749 1772.782 12.268 1772.825 150 12.860 3.465 1.999 869.626 21.413 7.681 557.207 0.000 8.836 0.049 220.749 1767.720 7.681 1767.736 160 12.860 3.759 1.367 869.626 24.934 3.789 557.207 0.000 8.836 0.049 220.749 1763.647 3.789 1763.651 170 12.860 3.939 0.693 869.626 27.213 1.076 557.207 0.000 8.836 0.049 220.749 1761.013 1.076 1761.013 180 12.860 4.000 0.002 869.626 27.998 0.000 557.207 0.000 8.836 0.049 220.749 1760.104 0.000 1760.104